diff --git a/doc/changelog.dox b/doc/changelog.dox
index edb2a8967..1b6e10446 100644
--- a/doc/changelog.dox
+++ b/doc/changelog.dox
@@ -416,6 +416,16 @@ See also:
     attributes and a @ref Shaders::PhongGL::Flag::Bitangent flag, implementing
     support for both four-component tangents (used by glTF, for example) and
     separate tangent and bitangent direction (used by Assimp).
+-   Added missing @ref Shaders::MeshVisualizerGL3D::setObjectId() "Shaders::MeshVisualizerGL*D::setObjectId()"
+    and a corresponding @ref Shaders::MeshVisualizerDrawUniform3D::objectId
+    "Shaders::MeshVisualizerDrawUniform*D::objectId"
+    member for UBO workflows. Originally the uniform wasn't present with the
+    assumption that users could easily adjust color map offset to achieve the
+    same effect. That was however unnecessarily annoying and error-prone in
+    cases where it's essential to have the same object IDs from multiple
+    draws have a matching color, and it was complicating multidraw workflows as
+    the color map offset was not a part of per-draw data, but rather material
+    data.
 
 @subsubsection changelog-latest-changes-trade Trade library
 
diff --git a/src/Magnum/Shaders/MeshVisualizer.frag b/src/Magnum/Shaders/MeshVisualizer.frag
index db16422a8..2cb67b5a0 100644
--- a/src/Magnum/Shaders/MeshVisualizer.frag
+++ b/src/Magnum/Shaders/MeshVisualizer.frag
@@ -43,7 +43,7 @@
 /* Uniforms */
 
 #ifndef UNIFORM_BUFFERS
-#if (defined(WIREFRAME_RENDERING) || defined(INSTANCED_OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)) && !defined(TBN_DIRECTION)
+#if (defined(WIREFRAME_RENDERING) || defined(OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)) && !defined(TBN_DIRECTION)
 #ifdef EXPLICIT_UNIFORM_LOCATION
 layout(location = 1)
 #endif
@@ -74,7 +74,7 @@ uniform lowp float wireframeWidth
     ;
 #elif defined(TBN_DIRECTION)
 #ifdef EXPLICIT_UNIFORM_LOCATION
-layout(location = 9)
+layout(location = 10)
 #endif
 uniform lowp float lineWidth
     #ifndef GL_ES
@@ -94,7 +94,7 @@ uniform lowp float smoothness
     ;
 #endif
 
-#if defined(INSTANCED_OBJECT_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
+#if defined(OBJECT_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
 #ifdef EXPLICIT_UNIFORM_LOCATION
 layout(location = 5)
 #endif
@@ -107,6 +107,14 @@ uniform lowp vec2 colorMapOffsetScale
 #define colorMapScale colorMapOffsetScale.y
 #endif
 
+#ifdef OBJECT_ID
+#ifdef EXPLICIT_UNIFORM_LOCATION
+layout(location = 6)
+#endif
+/* mediump is just 2^10, which might not be enough, this is 2^16 */
+uniform highp uint objectId; /* defaults to zero */
+#endif
+
 /* Uniform buffers */
 
 #else
@@ -136,8 +144,9 @@ struct DrawUniform {
     #elif !defined(TWO_DIMENSIONS)
     #error
     #endif
-    highp uvec4 materialIdReservedReservedReservedReserved;
-    #define draw_materialIdReserved materialIdReservedReservedReservedReserved.x
+    highp uvec4 materialIdReservedObjectIdReservedReserved;
+    #define draw_materialIdReserved materialIdReservedObjectIdReservedReserved.x
+    #define draw_objectId materialIdReservedObjectIdReservedReserved.y
 };
 
 layout(std140
@@ -175,7 +184,7 @@ layout(std140
 
 /* Textures */
 
-#if defined(INSTANCED_OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
+#if defined(OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
 #ifdef EXPLICIT_BINDING
 layout(binding = 4)
 #endif
@@ -225,12 +234,15 @@ out lowp vec4 fragmentColor;
 
 void main() {
     #ifdef UNIFORM_BUFFERS
+    #ifdef OBJECT_ID
+    highp const uint objectId = draws[drawId].draw_objectId;
+    #endif
     #if MATERIAL_COUNT > 1
     mediump const uint materialId = draws[drawId].draw_materialIdReserved & 0xffffu;
     #else
     #define materialId 0u
     #endif
-    #if (defined(WIREFRAME_RENDERING) || defined(INSTANCED_OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)) && !defined(TBN_DIRECTION)
+    #if (defined(WIREFRAME_RENDERING) || defined(OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)) && !defined(TBN_DIRECTION)
     lowp const vec4 color = materials[materialId].color;
     lowp const vec4 wireframeColor = materials[materialId].wireframeColor;
     #endif
@@ -242,7 +254,7 @@ void main() {
     #if defined(WIREFRAME_RENDERING) || defined(TBN_DIRECTION)
     lowp const float smoothness = materials[materialId].material_smoothness;
     #endif
-    #if defined(INSTANCED_OBJECT_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
+    #if defined(OBJECT_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
     lowp const float colorMapOffset = materials[materialId].material_colorMapOffset;
     lowp const float colorMapScale = materials[materialId].material_colorMapScale;
     #endif
@@ -251,14 +263,17 @@ void main() {
     /* Map object/vertex/primitive ID to a color. Will be either combined with
        the wireframe background color (if wireframe is enabled), ignored (if
        rendering TBN direction) or used as-is if nothing else is enabled */
-    #if defined(INSTANCED_OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
+    #if defined(OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
     lowp vec4 faceColor = texture(colorMapTexture, vec2(
         /* Object/primitive IDs are constant across the whole primitive so we
            do the offset/scale mapping here */
-        #if defined(INSTANCED_OBJECT_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
+        #if defined(OBJECT_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
         colorMapOffset + float(
-            #ifdef INSTANCED_OBJECT_ID
-            interpolatedInstanceObjectId
+            #ifdef OBJECT_ID
+            objectId
+                #ifdef INSTANCED_OBJECT_ID
+                + interpolatedInstanceObjectId
+                #endif
             #elif defined(PRIMITIVE_ID)
             gl_PrimitiveID
             #elif defined(PRIMITIVE_ID_FROM_VERTEX_ID)
@@ -312,7 +327,7 @@ void main() {
     #else
     fragmentColor = backgroundColor;
     #endif
-    #if defined(INSTANCED_OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
+    #if defined(OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
     fragmentColor *= faceColor;
     #endif
 
@@ -362,7 +377,7 @@ void main() {
     #endif
 
     /* Object / Vertex / Primitive ID visualization using a colormap */
-    #elif defined(INSTANCED_OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
+    #elif defined(OBJECT_ID) || defined(VERTEX_ID) || defined(PRIMITIVE_ID) || defined(PRIMITIVE_ID_FROM_VERTEX_ID)
     fragmentColor = color*faceColor;
 
     #else
diff --git a/src/Magnum/Shaders/MeshVisualizer.geom b/src/Magnum/Shaders/MeshVisualizer.geom
index ac662e2ad..e2a31d8f1 100644
--- a/src/Magnum/Shaders/MeshVisualizer.geom
+++ b/src/Magnum/Shaders/MeshVisualizer.geom
@@ -66,7 +66,7 @@ uniform lowp vec4 wireframeColor
 
 #if defined(TANGENT_DIRECTION) || defined(BITANGENT_DIRECTION) || defined(NORMAL_DIRECTION)
 #ifdef EXPLICIT_UNIFORM_LOCATION
-layout(location = 9)
+layout(location = 10)
 #endif
 uniform lowp float lineWidth
     #ifndef GL_ES
@@ -108,8 +108,9 @@ struct DrawUniform {
     #elif !defined(TWO_DIMENSIONS)
     #error
     #endif
-    highp uvec4 materialIdReservedReservedReservedReserved;
-    #define draw_materialIdReserved materialIdReservedReservedReservedReserved.x
+    highp uvec4 materialIdReservedObjectIdReservedReserved;
+    #define draw_materialIdReserved materialIdReservedObjectIdReservedReserved.x
+    #define draw_objectId materialIdReservedObjectIdReservedReserved.y
 };
 
 layout(std140
diff --git a/src/Magnum/Shaders/MeshVisualizer.h b/src/Magnum/Shaders/MeshVisualizer.h
index 9b0a540c4..dc174dfc1 100644
--- a/src/Magnum/Shaders/MeshVisualizer.h
+++ b/src/Magnum/Shaders/MeshVisualizer.h
@@ -59,11 +59,12 @@ struct MeshVisualizerDrawUniform2D {
         _pad0{}, /* Otherwise it refuses to constexpr, on 3.8 at least */
         #endif
         materialId{0}
-        #if (defined(CORRADE_TARGET_CLANG) && __clang_major__ < 4) || (defined(CORRADE_TARGET_APPLE_CLANG) && __clang_major__ < 8)
-        #ifndef CORRADE_TARGET_BIG_ENDIAN
+        #if ((defined(CORRADE_TARGET_CLANG) && __clang_major__ < 4) || (defined(CORRADE_TARGET_APPLE_CLANG) && __clang_major__ < 8)) && !defined(CORRADE_TARGET_BIG_ENDIAN)
         , _pad0{}
         #endif
-        , _pad1{}, _pad2{}, _pad3{}
+        , objectId{0}
+        #if (defined(CORRADE_TARGET_CLANG) && __clang_major__ < 4) || (defined(CORRADE_TARGET_APPLE_CLANG) && __clang_major__ < 8)
+        , _pad1{}, _pad2{}
         #endif
         {}
 
@@ -88,6 +89,15 @@ struct MeshVisualizerDrawUniform2D {
         return *this;
     }
 
+    /**
+     * @brief Set the @ref objectId field
+     * @return Reference to self (for method chaining)
+     */
+    MeshVisualizerDrawUniform2D& setObjectId(UnsignedInt id) {
+        objectId = id;
+        return *this;
+    }
+
     /**
      * @}
      */
@@ -108,7 +118,7 @@ struct MeshVisualizerDrawUniform2D {
     /* This field is an UnsignedInt in the shader and materialId is extracted
        as (value & 0xffff), so the order has to be different on BE */
     #ifndef CORRADE_TARGET_BIG_ENDIAN
-    alignas(4) UnsignedShort materialId;
+    UnsignedShort materialId;
     /* warning: Member __pad0__ is not documented. FFS DOXYGEN WHY DO YOU THINK
        I MADE THOSE UNNAMED, YOU DUMB FOOL */
     #ifndef DOXYGEN_GENERATING_OUTPUT
@@ -119,7 +129,7 @@ struct MeshVisualizerDrawUniform2D {
         :16; /* reserved for skinOffset */
     #endif
     #else
-    alignas(4) UnsignedShort
+    UnsignedShort
         #if (defined(CORRADE_TARGET_CLANG) && __clang_major__ < 4) || (defined(CORRADE_TARGET_APPLE_CLANG) && __clang_major__ < 8)
         _pad0 /* Otherwise it refuses to constexpr, on 3.8 at least */
         #endif
@@ -127,6 +137,21 @@ struct MeshVisualizerDrawUniform2D {
     UnsignedShort materialId;
     #endif
 
+    /**
+     * @brief Object ID
+     *
+     * Unlike @ref materialId, this index is used only for the object ID
+     * visualization, not to access any other uniform data. Default value
+     * is @cpp 0 @ce.
+     *
+     * Used only if @ref MeshVisualizerGL2D::Flag::ObjectId is enabled, ignored
+     * otherwise. If @ref MeshVisualizerGL2D::Flag::InstancedObjectId is
+     * enabled as well, this value is added to the ID coming from the
+     * @ref MeshVisualizerGL2D::ObjectId attribute.
+     * @see @ref MeshVisualizerGL2D::setObjectId()
+     */
+    UnsignedInt objectId;
+
     /* warning: Member __pad1__ is not documented. FFS DOXYGEN WHY DO YOU THINK
        I MADE THOSE UNNAMED, YOU DUMB FOOL */
     #ifndef DOXYGEN_GENERATING_OUTPUT
@@ -140,11 +165,6 @@ struct MeshVisualizerDrawUniform2D {
         _pad2 /* Otherwise it refuses to constexpr, on 3.8 at least */
         #endif
         :32;
-    Int
-        #if (defined(CORRADE_TARGET_CLANG) && __clang_major__ < 4) || (defined(CORRADE_TARGET_APPLE_CLANG) && __clang_major__ < 8)
-        _pad3 /* Otherwise it refuses to constexpr, on 3.8 at least */
-        #endif
-        :32;
     #endif
 };
 
@@ -165,11 +185,12 @@ struct MeshVisualizerDrawUniform3D {
         , _pad0{} /* Otherwise it refuses to constexpr, on 3.8 at least */
         #endif
         , materialId{0}
-        #if (defined(CORRADE_TARGET_CLANG) && __clang_major__ < 4) || (defined(CORRADE_TARGET_APPLE_CLANG) && __clang_major__ < 8)
-        #ifndef CORRADE_TARGET_BIG_ENDIAN
+        #if ((defined(CORRADE_TARGET_CLANG) && __clang_major__ < 4) || (defined(CORRADE_TARGET_APPLE_CLANG) && __clang_major__ < 8)) && !defined(CORRADE_TARGET_BIG_ENDIAN)
         , _pad0{}
         #endif
-        , _pad1{}, _pad2{}, _pad3{}
+        , objectId{0}
+        #if (defined(CORRADE_TARGET_CLANG) && __clang_major__ < 4) || (defined(CORRADE_TARGET_APPLE_CLANG) && __clang_major__ < 8)
+        , _pad1{}, _pad2{}
         #endif
         {}
 
@@ -206,6 +227,15 @@ struct MeshVisualizerDrawUniform3D {
         return *this;
     }
 
+    /**
+     * @brief Set the @ref objectId field
+     * @return Reference to self (for method chaining)
+     */
+    MeshVisualizerDrawUniform3D& setObjectId(UnsignedInt id) {
+        objectId = id;
+        return *this;
+    }
+
     /**
      * @}
      */
@@ -252,6 +282,21 @@ struct MeshVisualizerDrawUniform3D {
     UnsignedShort materialId;
     #endif
 
+    /**
+     * @brief Object ID
+     *
+     * Unlike @ref materialId, this index is used only for the object ID
+     * visualization, not to access any other uniform data. Default value
+     * is @cpp 0 @ce.
+     *
+     * Used only if @ref MeshVisualizerGL3D::Flag::ObjectId is enabled, ignored
+     * otherwise. If @ref MeshVisualizerGL3D::Flag::InstancedObjectId is
+     * enabled as well, this value is added to the ID coming from the
+     * @ref MeshVisualizerGL3D::ObjectId attribute.
+     * @see @ref MeshVisualizerGL3D::setObjectId()
+     */
+    UnsignedInt objectId;
+
     /* warning: Member __pad1__ is not documented. FFS DOXYGEN WHY DO YOU THINK
        I MADE THOSE UNNAMED, YOU DUMB FOOL */
     #ifndef DOXYGEN_GENERATING_OUTPUT
@@ -265,11 +310,6 @@ struct MeshVisualizerDrawUniform3D {
         _pad2 /* Otherwise it refuses to constexpr, on 3.8 at least */
         #endif
         :32;
-    Int
-        #if (defined(CORRADE_TARGET_CLANG) && __clang_major__ < 4) || (defined(CORRADE_TARGET_APPLE_CLANG) && __clang_major__ < 8)
-        _pad3 /* Otherwise it refuses to constexpr, on 3.8 at least */
-        #endif
-        :32;
     #endif
 };
 
diff --git a/src/Magnum/Shaders/MeshVisualizer.vert b/src/Magnum/Shaders/MeshVisualizer.vert
index 91f2355e7..8e3a8732f 100644
--- a/src/Magnum/Shaders/MeshVisualizer.vert
+++ b/src/Magnum/Shaders/MeshVisualizer.vert
@@ -49,7 +49,7 @@
 #ifndef UNIFORM_BUFFERS
 #ifdef TWO_DIMENSIONS
 #ifdef EXPLICIT_UNIFORM_LOCATION
-layout(location = 6)
+layout(location = 7)
 #endif
 uniform highp mat3 transformationProjectionMatrix
     #ifndef GL_ES
@@ -58,7 +58,7 @@ uniform highp mat3 transformationProjectionMatrix
     ;
 #elif defined(THREE_DIMENSIONS)
 #ifdef EXPLICIT_UNIFORM_LOCATION
-layout(location = 6)
+layout(location = 7)
 #endif
 uniform highp mat4 transformationMatrix
     #ifndef GL_ES
@@ -66,7 +66,7 @@ uniform highp mat4 transformationMatrix
     #endif
     ;
 #ifdef EXPLICIT_UNIFORM_LOCATION
-layout(location = 7)
+layout(location = 8)
 #endif
 uniform highp mat4 projectionMatrix
     #ifndef GL_ES
@@ -92,7 +92,7 @@ uniform lowp vec2 colorMapOffsetScale
 
 #if defined(TANGENT_DIRECTION) || defined(BITANGENT_FROM_TANGENT_DIRECTION) || defined(BITANGENT_DIRECTION) || defined(NORMAL_DIRECTION)
 #ifdef EXPLICIT_UNIFORM_LOCATION
-layout(location = 8)
+layout(location = 9)
 #endif
 uniform highp mat3 normalMatrix
     #ifndef GL_ES
@@ -101,7 +101,7 @@ uniform highp mat3 normalMatrix
     ;
 
 #ifdef EXPLICIT_UNIFORM_LOCATION
-layout(location = 10)
+layout(location = 11)
 #endif
 uniform highp float lineLength
     #ifndef GL_ES
@@ -166,8 +166,9 @@ struct DrawUniform {
     #elif !defined(TWO_DIMENSIONS)
     #error
     #endif
-    highp uvec4 materialIdReservedReservedReservedReserved;
-    #define draw_materialIdReserved materialIdReservedReservedReservedReserved.x
+    highp uvec4 materialIdReservedObjectIdReservedReserved;
+    #define draw_materialIdReserved materialIdReservedObjectIdReservedReserved.x
+    #define draw_objectId materialIdReservedObjectIdReservedReserved.y
 };
 
 layout(std140
diff --git a/src/Magnum/Shaders/MeshVisualizerGL.cpp b/src/Magnum/Shaders/MeshVisualizerGL.cpp
index 1fc40b8ec..9a61eee5d 100644
--- a/src/Magnum/Shaders/MeshVisualizerGL.cpp
+++ b/src/Magnum/Shaders/MeshVisualizerGL.cpp
@@ -85,12 +85,12 @@ MeshVisualizerGLBase::MeshVisualizerGLBase(FlagsBase flags
     #ifndef MAGNUM_TARGET_GLES2
     #ifndef CORRADE_NO_ASSERT
     Int countMutuallyExclusive = 0;
-    if(flags & FlagBase::InstancedObjectId) ++countMutuallyExclusive;
+    if(flags & FlagBase::ObjectId) ++countMutuallyExclusive;
     if(flags & FlagBase::VertexId) ++countMutuallyExclusive;
     if(flags & FlagBase::PrimitiveIdFromVertexId) ++countMutuallyExclusive;
     #endif
     CORRADE_ASSERT(countMutuallyExclusive <= 1,
-        "Shaders::MeshVisualizerGL: Flag::InstancedObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive", );
+        "Shaders::MeshVisualizerGL: Flag::ObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive", );
     #endif
 
     #ifndef MAGNUM_TARGET_GLES
@@ -161,7 +161,7 @@ GL::Version MeshVisualizerGLBase::setupShaders(GL::Shader& vert, GL::Shader& fra
 
     vert.addSource(_flags & FlagBase::Wireframe ? "#define WIREFRAME_RENDERING\n" : "")
         #ifndef MAGNUM_TARGET_GLES2
-        .addSource(_flags & FlagBase::InstancedObjectId ? "#define INSTANCED_OBJECT_ID\n" : "")
+        .addSource(_flags >= FlagBase::InstancedObjectId ? "#define INSTANCED_OBJECT_ID\n" : "")
         .addSource(_flags & FlagBase::VertexId ? "#define VERTEX_ID\n" : "")
         .addSource(_flags >= FlagBase::PrimitiveIdFromVertexId ? "#define PRIMITIVE_ID_FROM_VERTEX_ID\n" : "")
         #endif
@@ -185,7 +185,8 @@ GL::Version MeshVisualizerGLBase::setupShaders(GL::Shader& vert, GL::Shader& fra
     #endif
     frag.addSource(_flags & FlagBase::Wireframe ? "#define WIREFRAME_RENDERING\n" : "")
         #ifndef MAGNUM_TARGET_GLES2
-        .addSource(_flags & FlagBase::InstancedObjectId ? "#define INSTANCED_OBJECT_ID\n" : "")
+        .addSource(_flags & FlagBase::ObjectId ? "#define OBJECT_ID\n" : "")
+        .addSource(_flags >= FlagBase::InstancedObjectId ? "#define INSTANCED_OBJECT_ID\n" : "")
         .addSource(_flags & FlagBase::VertexId ? "#define VERTEX_ID\n" : "")
         .addSource(_flags & FlagBase::PrimitiveId ?
             (_flags >= FlagBase::PrimitiveIdFromVertexId ?
@@ -208,13 +209,24 @@ GL::Version MeshVisualizerGLBase::setupShaders(GL::Shader& vert, GL::Shader& fra
     return version;
 }
 
+#ifndef MAGNUM_TARGET_GLES2
+MeshVisualizerGLBase& MeshVisualizerGLBase::setObjectId(UnsignedInt id) {
+    CORRADE_ASSERT(!(_flags >= FlagBase::UniformBuffers),
+        "Shaders::MeshVisualizerGL::setObjectId(): the shader was created with uniform buffers enabled", *this);
+    CORRADE_ASSERT(_flags & FlagBase::ObjectId,
+        "Shaders::MeshVisualizerGL::setObjectId(): the shader was not created with object ID enabled", *this);
+    setUniform(_objectIdUniform, id);
+    return *this;
+}
+#endif
+
 MeshVisualizerGLBase& MeshVisualizerGLBase::setColor(const Color4& color) {
     #ifndef MAGNUM_TARGET_GLES2
     CORRADE_ASSERT(!(_flags >= FlagBase::UniformBuffers),
         "Shaders::MeshVisualizerGL::setColor(): the shader was created with uniform buffers enabled", *this);
     #endif
     #ifndef MAGNUM_TARGET_GLES2
-    CORRADE_ASSERT(_flags & (FlagBase::Wireframe|FlagBase::InstancedObjectId|FlagBase::VertexId|FlagBase::PrimitiveId),
+    CORRADE_ASSERT(_flags & (FlagBase::Wireframe|FlagBase::ObjectId|FlagBase::VertexId|FlagBase::PrimitiveId),
         "Shaders::MeshVisualizerGL::setColor(): the shader was not created with wireframe or object/vertex/primitive ID enabled", *this);
     #else
     CORRADE_ASSERT(_flags & FlagBase::Wireframe,
@@ -250,7 +262,7 @@ MeshVisualizerGLBase& MeshVisualizerGLBase::setWireframeWidth(const Float width)
 MeshVisualizerGLBase& MeshVisualizerGLBase::setColorMapTransformation(const Float offset, const Float scale) {
     CORRADE_ASSERT(!(_flags >= FlagBase::UniformBuffers),
         "Shaders::MeshVisualizerGL::setColorMapTransformation(): the shader was created with uniform buffers enabled", *this);
-    CORRADE_ASSERT(_flags & (FlagBase::InstancedObjectId|FlagBase::VertexId|FlagBase::PrimitiveId),
+    CORRADE_ASSERT(_flags & (FlagBase::ObjectId|FlagBase::VertexId|FlagBase::PrimitiveId),
         "Shaders::MeshVisualizerGL::setColorMapTransformation(): the shader was not created with object/vertex/primitive ID enabled", *this);
     setUniform(_colorMapOffsetScaleUniform, Vector2{offset, scale});
     return *this;
@@ -284,7 +296,7 @@ MeshVisualizerGLBase& MeshVisualizerGLBase::bindMaterialBuffer(GL::Buffer& buffe
 
 #ifndef MAGNUM_TARGET_GLES2
 MeshVisualizerGLBase& MeshVisualizerGLBase::bindColorMapTexture(GL::Texture2D& texture) {
-    CORRADE_ASSERT(_flags & (FlagBase::InstancedObjectId|FlagBase::VertexId|FlagBase::PrimitiveId),
+    CORRADE_ASSERT(_flags & (FlagBase::ObjectId|FlagBase::VertexId|FlagBase::PrimitiveId),
         "Shaders::MeshVisualizerGL::bindColorMapTexture(): the shader was not created with object/vertex/primitive ID enabled", *this);
     texture.bind(ColorMapTextureUnit);
     return *this;
@@ -303,7 +315,7 @@ MeshVisualizerGL2D::MeshVisualizerGL2D(const Flags flags
     #endif
 } {
     #ifndef MAGNUM_TARGET_GLES2
-    CORRADE_ASSERT(flags & ((Flag::Wireframe|Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId) & ~Flag::NoGeometryShader),
+    CORRADE_ASSERT(flags & ((Flag::Wireframe|Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId) & ~Flag::NoGeometryShader),
         "Shaders::MeshVisualizerGL2D: at least one visualization feature has to be enabled", );
     #else
     CORRADE_ASSERT(flags & (Flag::Wireframe & ~Flag::NoGeometryShader),
@@ -356,7 +368,7 @@ MeshVisualizerGL2D::MeshVisualizerGL2D(const Flags flags
         geom = Implementation::createCompatibilityShader(rs, version, GL::Shader::Type::Geometry);
         (*geom)
             .addSource("#define WIREFRAME_RENDERING\n#define MAX_VERTICES 3\n")
-            .addSource(_flags & FlagBase::InstancedObjectId ? "#define INSTANCED_OBJECT_ID\n" : "")
+            .addSource(_flags >= FlagBase::InstancedObjectId ? "#define INSTANCED_OBJECT_ID\n" : "")
             .addSource(_flags & FlagBase::VertexId ? "#define VERTEX_ID\n" : "")
             .addSource(_flags & FlagBase::PrimitiveId ?
                 (_flags >= FlagBase::PrimitiveIdFromVertexId ?
@@ -433,7 +445,7 @@ MeshVisualizerGL2D::MeshVisualizerGL2D(const Flags flags
             _transformationProjectionMatrixUniform = uniformLocation("transformationProjectionMatrix");
             if(flags & (Flag::Wireframe
                 #ifndef MAGNUM_TARGET_GLES2
-                |Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId
+                |Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId
                 #endif
             ))
                 _colorUniform = uniformLocation("color");
@@ -443,9 +455,11 @@ MeshVisualizerGL2D::MeshVisualizerGL2D(const Flags flags
                 _smoothnessUniform = uniformLocation("smoothness");
             }
             #ifndef MAGNUM_TARGET_GLES2
-            if(flags & (Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId)) {
+            if(flags & (Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId)) {
                 _colorMapOffsetScaleUniform = uniformLocation("colorMapOffsetScale");
             }
+            if(flags & Flag::ObjectId)
+                _objectIdUniform = uniformLocation("objectId");
             #endif
         }
     }
@@ -455,7 +469,7 @@ MeshVisualizerGL2D::MeshVisualizerGL2D(const Flags flags
     if(flags && !context.isExtensionSupported<GL::Extensions::ARB::shading_language_420pack>(version))
     #endif
     {
-        if(flags & (Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId)) {
+        if(flags & (Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId)) {
             setUniform(uniformLocation("colorMapTexture"), ColorMapTextureUnit);
         }
         #ifndef MAGNUM_TARGET_GLES2
@@ -480,7 +494,7 @@ MeshVisualizerGL2D::MeshVisualizerGL2D(const Flags flags
         setTransformationProjectionMatrix(Matrix3{Math::IdentityInit});
         if(flags & (Flag::Wireframe
             #ifndef MAGNUM_TARGET_GLES2
-            |Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId
+            |Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId
             #endif
         ))
             setColor(Color3(1.0f));
@@ -491,7 +505,7 @@ MeshVisualizerGL2D::MeshVisualizerGL2D(const Flags flags
             setSmoothness(2.0f);
         }
         #ifndef MAGNUM_TARGET_GLES2
-        if(flags & (Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId))
+        if(flags & (Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId))
             setColorMapTransformation(1.0f/512.0f, 1.0f/256.0f);
         #endif
     }
@@ -572,14 +586,14 @@ MeshVisualizerGL3D::MeshVisualizerGL3D(const Flags flags
     #endif
 } {
     #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
-    CORRADE_ASSERT(flags & ((Flag::Wireframe|Flag::TangentDirection|Flag::BitangentFromTangentDirection|Flag::BitangentDirection|Flag::NormalDirection|Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId) & ~Flag::NoGeometryShader),
+    CORRADE_ASSERT(flags & ((Flag::Wireframe|Flag::TangentDirection|Flag::BitangentFromTangentDirection|Flag::BitangentDirection|Flag::NormalDirection|Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId) & ~Flag::NoGeometryShader),
         "Shaders::MeshVisualizerGL3D: at least one visualization feature has to be enabled", );
     CORRADE_ASSERT(!(flags & Flag::NoGeometryShader && flags & (Flag::TangentDirection|Flag::BitangentFromTangentDirection|Flag::BitangentDirection|Flag::NormalDirection)),
         "Shaders::MeshVisualizerGL3D: geometry shader has to be enabled when rendering TBN direction", );
     CORRADE_ASSERT(!(flags & Flag::BitangentDirection && flags & Flag::BitangentFromTangentDirection),
         "Shaders::MeshVisualizerGL3D: Flag::BitangentDirection and Flag::BitangentFromTangentDirection are mutually exclusive", );
     #elif !defined(MAGNUM_TARGET_GLES2)
-    CORRADE_ASSERT(flags & ((Flag::Wireframe|Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId) & ~Flag::NoGeometryShader),
+    CORRADE_ASSERT(flags & ((Flag::Wireframe|Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId) & ~Flag::NoGeometryShader),
         "Shaders::MeshVisualizerGL3D: at least one visualization feature has to be enabled", );
     #else
     CORRADE_ASSERT(flags & (Flag::Wireframe & ~Flag::NoGeometryShader),
@@ -587,7 +601,7 @@ MeshVisualizerGL3D::MeshVisualizerGL3D(const Flags flags
     #endif
 
     #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
-    CORRADE_ASSERT(!(flags & Flag::InstancedObjectId) || !(flags & Flag::BitangentDirection),
+    CORRADE_ASSERT(!(flags >= Flag::InstancedObjectId) || !(flags & Flag::BitangentDirection),
         "Shaders::MeshVisualizerGL3D: Bitangent attribute binding conflicts with the ObjectId attribute, use a Tangent4 attribute with instanced object ID rendering instead", );
     #endif
 
@@ -669,7 +683,7 @@ MeshVisualizerGL3D::MeshVisualizerGL3D(const Flags flags
         (*geom)
             .addSource(Utility::formatString("#define MAX_VERTICES {}\n", maxVertices))
             .addSource(flags & Flag::Wireframe ? "#define WIREFRAME_RENDERING\n" : "")
-            .addSource(_flags & FlagBase::InstancedObjectId ? "#define INSTANCED_OBJECT_ID\n" : "")
+            .addSource(_flags >= FlagBase::InstancedObjectId ? "#define INSTANCED_OBJECT_ID\n" : "")
             .addSource(_flags & FlagBase::VertexId ? "#define VERTEX_ID\n" : "")
             .addSource(_flags & FlagBase::PrimitiveId ?
                 (_flags >= FlagBase::PrimitiveIdFromVertexId ?
@@ -765,7 +779,7 @@ MeshVisualizerGL3D::MeshVisualizerGL3D(const Flags flags
             _projectionMatrixUniform = uniformLocation("projectionMatrix");
             if(flags & (Flag::Wireframe
                 #ifndef MAGNUM_TARGET_GLES2
-                |Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId
+                |Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId
                 #endif
             ))
                 _colorUniform = uniformLocation("color");
@@ -781,9 +795,11 @@ MeshVisualizerGL3D::MeshVisualizerGL3D(const Flags flags
                 _smoothnessUniform = uniformLocation("smoothness");
             }
             #ifndef MAGNUM_TARGET_GLES2
-            if(flags & (Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId)) {
+            if(flags & (Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId)) {
                 _colorMapOffsetScaleUniform = uniformLocation("colorMapOffsetScale");
             }
+            if(flags & Flag::ObjectId)
+                _objectIdUniform = uniformLocation("objectId");
             #endif
             #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
             if(flags & (Flag::TangentDirection|Flag::BitangentFromTangentDirection|Flag::BitangentDirection|Flag::NormalDirection)) {
@@ -800,7 +816,7 @@ MeshVisualizerGL3D::MeshVisualizerGL3D(const Flags flags
     if(flags && !context.isExtensionSupported<GL::Extensions::ARB::shading_language_420pack>(version))
     #endif
     {
-        if(flags & (Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId)) {
+        if(flags & (Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId)) {
             setUniform(uniformLocation("colorMapTexture"), ColorMapTextureUnit);
         }
         #ifndef MAGNUM_TARGET_GLES2
@@ -827,7 +843,7 @@ MeshVisualizerGL3D::MeshVisualizerGL3D(const Flags flags
         setProjectionMatrix(Matrix4{Math::IdentityInit});
         if(flags & (Flag::Wireframe
             #ifndef MAGNUM_TARGET_GLES2
-            |Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId
+            |Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId
             #endif
         ))
             setColor(Color3(1.0f));
@@ -844,7 +860,7 @@ MeshVisualizerGL3D::MeshVisualizerGL3D(const Flags flags
             setSmoothness(2.0f);
         }
         #ifndef MAGNUM_TARGET_GLES2
-        if(flags & (Flag::InstancedObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId))
+        if(flags & (Flag::ObjectId|Flag::VertexId|Flag::PrimitiveIdFromVertexId))
             setColorMapTransformation(1.0f/512.0f, 1.0f/256.0f);
         #endif
         #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
@@ -996,6 +1012,7 @@ Debug& operator<<(Debug& debug, const MeshVisualizerGL2D::Flag value) {
         _c(NoGeometryShader)
         _c(Wireframe)
         #ifndef MAGNUM_TARGET_GLES2
+        _c(ObjectId)
         _c(InstancedObjectId)
         _c(VertexId)
         #ifndef MAGNUM_TARGET_WEBGL
@@ -1029,6 +1046,7 @@ Debug& operator<<(Debug& debug, const MeshVisualizerGL3D::Flag value) {
         _c(NormalDirection)
         #endif
         #ifndef MAGNUM_TARGET_GLES2
+        _c(ObjectId)
         _c(InstancedObjectId)
         _c(VertexId)
         #ifndef MAGNUM_TARGET_WEBGL
@@ -1054,7 +1072,8 @@ Debug& operator<<(Debug& debug, const MeshVisualizerGL2D::Flags value) {
            there */
         MeshVisualizerGL2D::Flag::NoGeometryShader,
         #ifndef MAGNUM_TARGET_GLES2
-        MeshVisualizerGL2D::Flag::InstancedObjectId,
+        MeshVisualizerGL2D::Flag::InstancedObjectId, /* Superset of ObjectId */
+        MeshVisualizerGL2D::Flag::ObjectId,
         MeshVisualizerGL2D::Flag::VertexId,
         MeshVisualizerGL2D::Flag::PrimitiveIdFromVertexId, /* Superset of PrimitiveId */
         #ifndef MAGNUM_TARGET_WEBGL
@@ -1081,7 +1100,8 @@ Debug& operator<<(Debug& debug, const MeshVisualizerGL3D::Flags value) {
         MeshVisualizerGL3D::Flag::NormalDirection,
         #endif
         #ifndef MAGNUM_TARGET_GLES2
-        MeshVisualizerGL3D::Flag::InstancedObjectId,
+        MeshVisualizerGL3D::Flag::InstancedObjectId, /* Superset of ObjectId */
+        MeshVisualizerGL3D::Flag::ObjectId,
         MeshVisualizerGL3D::Flag::VertexId,
         MeshVisualizerGL3D::Flag::PrimitiveIdFromVertexId, /* Superset of PrimitiveId */
         #ifndef MAGNUM_TARGET_WEBGL
diff --git a/src/Magnum/Shaders/MeshVisualizerGL.h b/src/Magnum/Shaders/MeshVisualizerGL.h
index 1b2dda3ed..8f9b8e228 100644
--- a/src/Magnum/Shaders/MeshVisualizerGL.h
+++ b/src/Magnum/Shaders/MeshVisualizerGL.h
@@ -50,7 +50,8 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGLBase: public GL::AbstractShaderProgr
             Wireframe = 1 << 0,
             NoGeometryShader = 1 << 1,
             #ifndef MAGNUM_TARGET_GLES2
-            InstancedObjectId = 1 << 2,
+            ObjectId = 1 << 12,
+            InstancedObjectId = (1 << 2)|ObjectId,
             VertexId = 1 << 3,
             PrimitiveId = 1 << 4,
             PrimitiveIdFromVertexId = (1 << 5)|PrimitiveId,
@@ -72,6 +73,7 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGLBase: public GL::AbstractShaderProgr
 
         MAGNUM_SHADERS_LOCAL GL::Version setupShaders(GL::Shader& vert, GL::Shader& frag, const Utility::Resource& rs) const;
 
+        MeshVisualizerGLBase& setObjectId(UnsignedInt id);
         MeshVisualizerGLBase& setColor(const Color4& color);
         MeshVisualizerGLBase& setWireframeColor(const Color4& color);
         MeshVisualizerGLBase& setWireframeWidth(Float width);
@@ -104,7 +106,8 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGLBase: public GL::AbstractShaderProgr
             _wireframeWidthUniform{3},
             _smoothnessUniform{4};
         #ifndef MAGNUM_TARGET_GLES2
-        Int _colorMapOffsetScaleUniform{5};
+        Int _colorMapOffsetScaleUniform{5},
+            _objectIdUniform{6};
         /* Used instead of all other uniforms except viewportSize when
            Flag::UniformBuffers is set, so it can alias them */
         Int _drawOffsetUniform{1};
@@ -208,8 +211,37 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGL2D: public Implementation::MeshVisua
             NoGeometryShader = 1 << 1,
 
             #ifndef MAGNUM_TARGET_GLES2
-            /** @copydoc MeshVisualizerGL3D::Flag::InstancedObjectId */
-            InstancedObjectId = 1 << 2,
+            /**
+             * Visualize object ID set via @ref setObjectId() or
+             * @ref MeshVisualizerDrawUniform2D::objectId. Since the ID is
+             * uniform for the whole draw, this feature is mainly useful in
+             * multidraw scenarios or when combined with
+             * @ref Flag::InstancedObjectId. Mutually exclusive with
+             * @ref Flag::VertexId and @ref Flag::PrimitiveId.
+             * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
+             * @requires_gles30 Object ID input requires integer support in
+             *      shaders, which is not available in OpenGL ES 2.0.
+             * @requires_webgl20 Object ID input requires integer support in
+             *      shaders, which is not available in WebGL 1.0.
+             * @m_since_latest
+             */
+            ObjectId = 1 << 12,
+
+            /**
+             * Visualize instanced object ID. You need to provide the
+             * @ref ObjectId attribute in the mesh, which then gets summed with
+             * the ID coming from @ref setObjectId() or
+             * @ref MeshVisualizerDrawUniform2D::objectId. Implicitly enables
+             * @ref Flag::ObjectId. Mutually exclusive with @ref Flag::VertexId
+             * and @ref Flag::PrimitiveId.
+             * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
+             * @requires_gles30 Object ID input requires integer support in
+             *      shaders, which is not available in OpenGL ES 2.0.
+             * @requires_webgl20 Object ID input requires integer support in
+             *      shaders, which is not available in WebGL 1.0.
+             * @m_since{2020,06}
+             */
+            InstancedObjectId = (1 << 2)|ObjectId,
 
             /** @copydoc MeshVisualizerGL3D::Flag::VertexId */
             VertexId = 1 << 3,
@@ -406,6 +438,28 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGL2D: public Implementation::MeshVisua
          */
         MeshVisualizerGL2D& setViewportSize(const Vector2& size);
 
+        /**
+         * @brief Set object ID
+         * @return Reference to self (for method chaining)
+         * @m_since_latest
+         *
+         * Expects that @ref Flag::ObjectId is enabled. Default is
+         * @cpp 0 @ce. If @ref Flag::InstancedObjectId is enabled as well, this
+         * value is added to the ID coming from the @ref ObjectId attribute.
+         *
+         * Expects that @ref Flag::UniformBuffers is not set, in that case fill
+         * @ref MeshVisualizerDrawUniform2D::objectId and call
+         * @ref bindDrawBuffer() instead.
+         * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
+         * @requires_gles30 Object ID input requires integer support in
+         *      shaders, which is not available in OpenGL ES 2.0.
+         * @requires_webgl20 Object ID input requires integer support in
+         *      shaders, which is not available in WebGL 1.0.
+         */
+        MeshVisualizerGL2D& setObjectId(UnsignedInt id) {
+            return static_cast<MeshVisualizerGL2D&>(Implementation::MeshVisualizerGLBase::setObjectId(id));
+        }
+
         /**
          * @brief Set base object color
          * @return Reference to self (for method chaining)
@@ -633,7 +687,7 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGL2D: public Implementation::MeshVisua
         #endif
 
     private:
-        Int _transformationProjectionMatrixUniform{6};
+        Int _transformationProjectionMatrixUniform{7};
 };
 
 /**
@@ -960,17 +1014,36 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGL3D: public Implementation::MeshVisua
 
             #ifndef MAGNUM_TARGET_GLES2
             /**
-             * Visualize instanced object ID. You need to provide the
-             * @ref ObjectId attribute in the mesh. Mutually exclusive with
+             * Visualize object ID set via @ref setObjectId() or
+             * @ref MeshVisualizerDrawUniform3D::objectId. Since the ID is
+             * uniform for the whole draw, this feature is mainly useful in
+             * multidraw scenarios or when combined with
+             * @ref Flag::InstancedObjectId. Mutually exclusive with
              * @ref Flag::VertexId and @ref Flag::PrimitiveId.
              * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
-             * @requires_gles30 Object ID output requires integer support in
+             * @requires_gles30 Object ID input requires integer support in
              *      shaders, which is not available in OpenGL ES 2.0.
-             * @requires_webgl20 Object ID output requires integer support in
+             * @requires_webgl20 Object ID input requires integer support in
+             *      shaders, which is not available in WebGL 1.0.
+             * @m_since_latest
+             */
+            ObjectId = 1 << 12,
+
+            /**
+             * Visualize instanced object ID. You need to provide the
+             * @ref ObjectId attribute in the mesh, which then gets summed with
+             * the ID coming from @ref setObjectId() or
+             * @ref MeshVisualizerDrawUniform3D::objectId. Implicitly enables
+             * @ref Flag::ObjectId. Mutually exclusive with @ref Flag::VertexId
+             * and @ref Flag::PrimitiveId.
+             * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
+             * @requires_gles30 Object ID input requires integer support in
+             *      shaders, which is not available in OpenGL ES 2.0.
+             * @requires_webgl20 Object ID input requires integer support in
              *      shaders, which is not available in WebGL 1.0.
              * @m_since{2020,06}
              */
-            InstancedObjectId = 1 << 2,
+            InstancedObjectId = (1 << 2)|ObjectId,
 
             /**
              * Visualize vertex ID (@cpp gl_VertexID @ce). Useful for
@@ -1339,6 +1412,28 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGL3D: public Implementation::MeshVisua
          */
         MeshVisualizerGL3D& setViewportSize(const Vector2& size);
 
+        /**
+         * @brief Set object ID
+         * @return Reference to self (for method chaining)
+         * @m_since_latest
+         *
+         * Expects that @ref Flag::ObjectId is enabled. Default is
+         * @cpp 0 @ce. If @ref Flag::InstancedObjectId is enabled as well, this
+         * value is added to the ID coming from the @ref ObjectId attribute.
+         *
+         * Expects that @ref Flag::UniformBuffers is not set, in that case fill
+         * @ref MeshVisualizerDrawUniform3D::objectId and call
+         * @ref bindDrawBuffer() instead.
+         * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
+         * @requires_gles30 Object ID input requires integer support in
+         *      shaders, which is not available in OpenGL ES 2.0.
+         * @requires_webgl20 Object ID input requires integer support in
+         *      shaders, which is not available in WebGL 1.0.
+         */
+        MeshVisualizerGL3D& setObjectId(UnsignedInt id) {
+            return static_cast<MeshVisualizerGL3D&>(Implementation::MeshVisualizerGLBase::setObjectId(id));
+        }
+
         /**
          * @brief Set base object color
          * @return Reference to self (for method chaining)
@@ -1405,11 +1500,6 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGL3D: public Implementation::MeshVisua
          * @ref Flag::InstancedObjectId or @ref Flag::PrimitiveId /
          * @ref Flag::PrimitiveIdFromVertexId is enabled.
          *
-         * Note that this shader doesn't directly offer a
-         * @ref FlatGL::setObjectId() "setObjectId()" uniform that's used to
-         * offset the per-vertex / per-instance ID. Instead, you need to encode
-         * the base offset into the @p offset parameter.
-         *
          * Expects that @ref Flag::UniformBuffers is not set, in that case fill
          * @ref MeshVisualizerMaterialUniform::colorMapOffset and
          * @ref MeshVisualizerMaterialUniform::colorMapScale and call
@@ -1685,12 +1775,12 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGL3D: public Implementation::MeshVisua
         #endif
 
     private:
-        Int _transformationMatrixUniform{6},
-            _projectionMatrixUniform{7};
+        Int _transformationMatrixUniform{7},
+            _projectionMatrixUniform{8};
         #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
-        Int _normalMatrixUniform{8},
-            _lineWidthUniform{9},
-            _lineLengthUniform{10};
+        Int _normalMatrixUniform{9},
+            _lineWidthUniform{10},
+            _lineLengthUniform{11};
         #endif
 };
 
diff --git a/src/Magnum/Shaders/Test/CMakeLists.txt b/src/Magnum/Shaders/Test/CMakeLists.txt
index 90feea049..02e748404 100644
--- a/src/Magnum/Shaders/Test/CMakeLists.txt
+++ b/src/Magnum/Shaders/Test/CMakeLists.txt
@@ -199,6 +199,8 @@ if(BUILD_GL_TESTS)
             MeshVisualizerTestFiles/bitangents-from-tangents.tga
             MeshVisualizerTestFiles/defaults-instancedobjectid2D.tga
             MeshVisualizerTestFiles/defaults-instancedobjectid3D.tga
+            MeshVisualizerTestFiles/defaults-objectid2D.tga
+            MeshVisualizerTestFiles/defaults-objectid3D.tga
             MeshVisualizerTestFiles/defaults-primitiveid2D.tga
             MeshVisualizerTestFiles/defaults-primitiveid3D.tga
             MeshVisualizerTestFiles/defaults-tbn.tga
@@ -208,6 +210,8 @@ if(BUILD_GL_TESTS)
             MeshVisualizerTestFiles/defaults-wireframe3D.tga
             MeshVisualizerTestFiles/instancedobjectid2D.tga
             MeshVisualizerTestFiles/instancedobjectid3D.tga
+            MeshVisualizerTestFiles/objectid2D.tga
+            MeshVisualizerTestFiles/objectid3D.tga
             MeshVisualizerTestFiles/primitiveid-tn.tga
             MeshVisualizerTestFiles/primitiveid2D.tga
             MeshVisualizerTestFiles/primitiveid3D.tga
diff --git a/src/Magnum/Shaders/Test/MeshVisualizerGLTest.cpp b/src/Magnum/Shaders/Test/MeshVisualizerGLTest.cpp
index 3417e73d4..743eea173 100644
--- a/src/Magnum/Shaders/Test/MeshVisualizerGLTest.cpp
+++ b/src/Magnum/Shaders/Test/MeshVisualizerGLTest.cpp
@@ -115,6 +115,8 @@ struct MeshVisualizerGLTest: GL::OpenGLTester {
     void setWireframeNotEnabled2D();
     void setWireframeNotEnabled3D();
     #ifndef MAGNUM_TARGET_GLES2
+    void setObjectIdNotEnabled2D();
+    void setObjectIdNotEnabled3D();
     void setColorMapNotEnabled2D();
     void setColorMapNotEnabled3D();
     #endif
@@ -134,6 +136,8 @@ struct MeshVisualizerGLTest: GL::OpenGLTester {
     template<MeshVisualizerGL3D::Flag flag = MeshVisualizerGL3D::Flag{}> void renderDefaultsWireframe3D();
     #endif
     #ifndef MAGNUM_TARGET_GLES2
+    template<MeshVisualizerGL2D::Flag flag = MeshVisualizerGL2D::Flag{}> void renderDefaultsObjectId2D();
+    template<MeshVisualizerGL3D::Flag flag = MeshVisualizerGL3D::Flag{}> void renderDefaultsObjectId3D();
     template<MeshVisualizerGL2D::Flag flag = MeshVisualizerGL2D::Flag{}> void renderDefaultsInstancedObjectId2D();
     template<MeshVisualizerGL3D::Flag flag = MeshVisualizerGL3D::Flag{}> void renderDefaultsInstancedObjectId3D();
     template<MeshVisualizerGL2D::Flag flag = MeshVisualizerGL2D::Flag{}> void renderDefaultsVertexId2D();
@@ -215,6 +219,7 @@ constexpr struct {
     #endif
     {"wireframe w/o GS", MeshVisualizerGL2D::Flag::Wireframe|MeshVisualizerGL2D::Flag::NoGeometryShader},
     #ifndef MAGNUM_TARGET_GLES2
+    {"object ID", MeshVisualizerGL2D::Flag::ObjectId},
     {"instanced object ID", MeshVisualizerGL2D::Flag::InstancedObjectId},
     {"vertex ID", MeshVisualizerGL2D::Flag::VertexId},
     #ifndef MAGNUM_TARGET_WEBGL
@@ -245,6 +250,7 @@ constexpr struct {
     {"wireframe", MeshVisualizerGL2D::Flag::UniformBuffers|MeshVisualizerGL2D::Flag::Wireframe, 1, 1},
     #endif
     {"wireframe w/o GS", MeshVisualizerGL2D::Flag::UniformBuffers|MeshVisualizerGL2D::Flag::Wireframe|MeshVisualizerGL2D::Flag::NoGeometryShader, 1, 1},
+    {"object ID", MeshVisualizerGL2D::Flag::UniformBuffers|MeshVisualizerGL2D::Flag::ObjectId, 1, 1},
     {"instanced object ID", MeshVisualizerGL2D::Flag::UniformBuffers|MeshVisualizerGL2D::Flag::InstancedObjectId, 1, 1},
     {"vertex ID", MeshVisualizerGL2D::Flag::UniformBuffers|MeshVisualizerGL2D::Flag::VertexId, 1, 1},
     #ifndef MAGNUM_TARGET_WEBGL
@@ -265,6 +271,7 @@ constexpr struct {
     #endif
     {"wireframe w/o GS", MeshVisualizerGL3D::Flag::Wireframe|MeshVisualizerGL3D::Flag::NoGeometryShader},
     #ifndef MAGNUM_TARGET_GLES2
+    {"object ID", MeshVisualizerGL3D::Flag::ObjectId},
     {"instanced object ID", MeshVisualizerGL3D::Flag::InstancedObjectId},
     {"vertex ID", MeshVisualizerGL3D::Flag::VertexId},
     #ifndef MAGNUM_TARGET_WEBGL
@@ -284,7 +291,9 @@ constexpr struct {
     {"wireframe + instanced object ID + T/N direction", MeshVisualizerGL3D::Flag::Wireframe|MeshVisualizerGL3D::Flag::InstancedObjectId|MeshVisualizerGL3D::Flag::TangentDirection|MeshVisualizerGL3D::Flag::NormalDirection},
     {"wireframe + vertex ID + T/B direction", MeshVisualizerGL3D::Flag::Wireframe|MeshVisualizerGL3D::Flag::VertexId|MeshVisualizerGL3D::Flag::TangentDirection|MeshVisualizerGL3D::Flag::BitangentDirection},
     /* InstancedObjectId|BitangentDirection is disallowed (checked in
-       ConstructInvalidData3D), but this should work */
+       ConstructInvalidData3D), but both ObjectId alone and
+       BitangentFromTangentDirection should work */
+    {"object ID + bitangent direction", MeshVisualizerGL3D::Flag::ObjectId|MeshVisualizerGL3D::Flag::BitangentDirection},
     {"instanced object ID + bitangent from tangent direction", MeshVisualizerGL3D::Flag::InstancedObjectId|MeshVisualizerGL3D::Flag::BitangentFromTangentDirection},
     #endif
 };
@@ -310,6 +319,7 @@ constexpr struct {
     {"wireframe", MeshVisualizerGL3D::Flag::UniformBuffers|MeshVisualizerGL3D::Flag::Wireframe, 1, 1},
     #endif
     {"wireframe w/o GS", MeshVisualizerGL3D::Flag::UniformBuffers|MeshVisualizerGL3D::Flag::Wireframe|MeshVisualizerGL3D::Flag::NoGeometryShader, 1, 1},
+    {"object ID", MeshVisualizerGL3D::Flag::UniformBuffers|MeshVisualizerGL3D::Flag::ObjectId, 1, 1},
     {"instanced object ID", MeshVisualizerGL3D::Flag::UniformBuffers|MeshVisualizerGL3D::Flag::InstancedObjectId, 1, 1},
     {"vertex ID", MeshVisualizerGL3D::Flag::UniformBuffers|MeshVisualizerGL3D::Flag::VertexId, 1, 1},
     #ifndef MAGNUM_TARGET_WEBGL
@@ -345,12 +355,15 @@ constexpr struct {
         #endif
         },
     #ifndef MAGNUM_TARGET_GLES2
+    {"both object and primitive ID",
+        MeshVisualizerGL2D::Flag::ObjectId|MeshVisualizerGL2D::Flag::PrimitiveIdFromVertexId,
+        ": Flag::ObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive"},
     {"both instanced object and primitive ID",
         MeshVisualizerGL2D::Flag::InstancedObjectId|MeshVisualizerGL2D::Flag::PrimitiveIdFromVertexId,
-        ": Flag::InstancedObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive"},
-    {"both instanced object and vertex ID",
-        MeshVisualizerGL2D::Flag::InstancedObjectId|MeshVisualizerGL2D::Flag::VertexId,
-        ": Flag::InstancedObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive"}
+        ": Flag::ObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive"},
+    {"both object and vertex ID",
+        MeshVisualizerGL2D::Flag::ObjectId|MeshVisualizerGL2D::Flag::VertexId,
+        ": Flag::ObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive"}
     #endif
 };
 
@@ -382,12 +395,15 @@ constexpr struct {
         #endif
         },
     #ifndef MAGNUM_TARGET_GLES2
+    {"both object and primitive ID",
+        MeshVisualizerGL3D::Flag::ObjectId|MeshVisualizerGL3D::Flag::PrimitiveIdFromVertexId,
+        ": Flag::ObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive"},
     {"both instanced object and primitive ID",
         MeshVisualizerGL3D::Flag::InstancedObjectId|MeshVisualizerGL3D::Flag::PrimitiveIdFromVertexId,
-        ": Flag::InstancedObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive"},
+        ": Flag::ObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive"},
     {"both vertex and primitive ID",
         MeshVisualizerGL3D::Flag::VertexId|MeshVisualizerGL3D::Flag::PrimitiveIdFromVertexId,
-        ": Flag::InstancedObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive"},
+        ": Flag::ObjectId, Flag::VertexId and Flag::PrimitiveId are mutually exclusive"},
     #endif
     #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
     {"geometry shader disabled but needed",
@@ -477,6 +493,10 @@ constexpr struct {
     const char* file2D;
     const char* file3D;
 } ObjectVertexPrimitiveIdData[] {
+    {"object ID",
+        MeshVisualizerGL2D::Flag::ObjectId,
+        MeshVisualizerGL3D::Flag::ObjectId,
+        "objectid2D.tga", "objectid3D.tga"},
     {"instanced object ID",
         MeshVisualizerGL2D::Flag::InstancedObjectId,
         MeshVisualizerGL3D::Flag::InstancedObjectId,
@@ -752,6 +772,8 @@ MeshVisualizerGLTest::MeshVisualizerGLTest() {
         &MeshVisualizerGLTest::setWireframeNotEnabled2D,
         &MeshVisualizerGLTest::setWireframeNotEnabled3D,
         #ifndef MAGNUM_TARGET_GLES2
+        &MeshVisualizerGLTest::setObjectIdNotEnabled2D,
+        &MeshVisualizerGLTest::setObjectIdNotEnabled3D,
         &MeshVisualizerGLTest::setColorMapNotEnabled2D,
         &MeshVisualizerGLTest::setColorMapNotEnabled3D,
         #endif
@@ -780,6 +802,22 @@ MeshVisualizerGLTest::MeshVisualizerGLTest() {
         &MeshVisualizerGLTest::renderTeardown);
     #endif
 
+    #ifndef MAGNUM_TARGET_GLES2
+    /* MSVC needs explicit type due to default template args */
+    addTests<MeshVisualizerGLTest>({
+        &MeshVisualizerGLTest::renderDefaultsObjectId2D,
+        #ifndef MAGNUM_TARGET_GLES2
+        &MeshVisualizerGLTest::renderDefaultsObjectId2D<MeshVisualizerGL2D::Flag::UniformBuffers>,
+        #endif
+        &MeshVisualizerGLTest::renderDefaultsObjectId3D,
+        #ifndef MAGNUM_TARGET_GLES2
+        &MeshVisualizerGLTest::renderDefaultsObjectId3D<MeshVisualizerGL3D::Flag::UniformBuffers>,
+        #endif
+        },
+        &MeshVisualizerGLTest::renderSetup,
+        &MeshVisualizerGLTest::renderTeardown);
+    #endif
+
     #ifndef MAGNUM_TARGET_GLES2
     /* MSVC needs explicit type due to default template args */
     addInstancedTests<MeshVisualizerGLTest>({
@@ -1394,6 +1432,7 @@ void MeshVisualizerGLTest::setUniformUniformBuffersEnabled2D() {
     MeshVisualizerGL2D shader{MeshVisualizerGL2D::Flag::UniformBuffers|MeshVisualizerGL2D::Flag::Wireframe|MeshVisualizerGL2D::Flag::NoGeometryShader};
     shader.setTransformationProjectionMatrix({})
         /* setViewportSize() works on both UBOs and classic */
+        .setObjectId({})
         .setColor({})
         .setWireframeColor({})
         .setWireframeWidth({})
@@ -1401,6 +1440,7 @@ void MeshVisualizerGLTest::setUniformUniformBuffersEnabled2D() {
         .setSmoothness({});
     CORRADE_COMPARE(out.str(),
         "Shaders::MeshVisualizerGL2D::setTransformationProjectionMatrix(): the shader was created with uniform buffers enabled\n"
+        "Shaders::MeshVisualizerGL::setObjectId(): the shader was created with uniform buffers enabled\n"
         "Shaders::MeshVisualizerGL::setColor(): the shader was created with uniform buffers enabled\n"
         "Shaders::MeshVisualizerGL::setWireframeColor(): the shader was created with uniform buffers enabled\n"
         "Shaders::MeshVisualizerGL::setWireframeWidth(): the shader was created with uniform buffers enabled\n"
@@ -1425,6 +1465,7 @@ void MeshVisualizerGLTest::setUniformUniformBuffersEnabled3D() {
     shader.setProjectionMatrix({})
         .setTransformationMatrix({})
         /* setViewportSize() works on both UBOs and classic */
+        .setObjectId({})
         .setColor({})
         .setWireframeColor({})
         .setWireframeWidth({})
@@ -1433,6 +1474,7 @@ void MeshVisualizerGLTest::setUniformUniformBuffersEnabled3D() {
     CORRADE_COMPARE(out.str(),
         "Shaders::MeshVisualizerGL3D::setProjectionMatrix(): the shader was created with uniform buffers enabled\n"
         "Shaders::MeshVisualizerGL3D::setTransformationMatrix(): the shader was created with uniform buffers enabled\n"
+        "Shaders::MeshVisualizerGL::setObjectId(): the shader was created with uniform buffers enabled\n"
         "Shaders::MeshVisualizerGL::setColor(): the shader was created with uniform buffers enabled\n"
         "Shaders::MeshVisualizerGL::setWireframeColor(): the shader was created with uniform buffers enabled\n"
         "Shaders::MeshVisualizerGL::setWireframeWidth(): the shader was created with uniform buffers enabled\n"
@@ -1582,6 +1624,32 @@ void MeshVisualizerGLTest::setWireframeNotEnabled3D() {
 }
 
 #ifndef MAGNUM_TARGET_GLES2
+void MeshVisualizerGLTest::setObjectIdNotEnabled2D() {
+    #ifdef CORRADE_NO_ASSERT
+    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
+    #endif
+
+    MeshVisualizerGL2D shader{NoCreate};
+
+    std::ostringstream out;
+    Error redirectError{&out};
+    shader.setObjectId({});
+    CORRADE_COMPARE(out.str(), "Shaders::MeshVisualizerGL::setObjectId(): the shader was not created with object ID enabled\n");
+}
+
+void MeshVisualizerGLTest::setObjectIdNotEnabled3D() {
+    #ifdef CORRADE_NO_ASSERT
+    CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
+    #endif
+
+    MeshVisualizerGL3D shader{NoCreate};
+
+    std::ostringstream out;
+    Error redirectError{&out};
+    shader.setObjectId({});
+    CORRADE_COMPARE(out.str(), "Shaders::MeshVisualizerGL::setObjectId(): the shader was not created with object ID enabled\n");
+}
+
 void MeshVisualizerGLTest::setColorMapNotEnabled2D() {
     #ifdef CORRADE_NO_ASSERT
     CORRADE_SKIP("CORRADE_NO_ASSERT defined, can't test assertions");
@@ -1919,6 +1987,114 @@ template<MeshVisualizerGL3D::Flag flag> void MeshVisualizerGLTest::renderDefault
 #endif
 
 #ifndef MAGNUM_TARGET_GLES2
+template<MeshVisualizerGL2D::Flag flag> void MeshVisualizerGLTest::renderDefaultsObjectId2D() {
+    if(flag == MeshVisualizerGL2D::Flag::UniformBuffers) {
+        setTestCaseTemplateName("Flag::UniformBuffers");
+
+        #ifndef MAGNUM_TARGET_GLES
+        if(!GL::Context::current().isExtensionSupported<GL::Extensions::ARB::uniform_buffer_object>())
+            CORRADE_SKIP(GL::Extensions::ARB::uniform_buffer_object::string() << "is not supported.");
+        #endif
+    }
+
+    #ifndef MAGNUM_TARGET_GLES
+    if(!GL::Context::current().isExtensionSupported<GL::Extensions::EXT::gpu_shader4>())
+        CORRADE_SKIP(GL::Extensions::EXT::gpu_shader4::string() << "is not supported.");
+    #endif
+
+    GL::Mesh circle = MeshTools::compile(Primitives::circle2DSolid(16));
+
+    MeshVisualizerGL2D shader{MeshVisualizerGL2D::Flag::ObjectId|flag};
+    shader.bindColorMapTexture(_colorMapTexture);
+
+    if(flag == MeshVisualizerGL2D::Flag{}) {
+        shader.draw(circle);
+    } else if(flag == MeshVisualizerGL2D::Flag::UniformBuffers) {
+        GL::Buffer transformationProjectionUniform{GL::Buffer::TargetHint::Uniform, {
+            TransformationProjectionUniform2D{}
+        }};
+        GL::Buffer drawUniform{GL::Buffer::TargetHint::Uniform, {
+            MeshVisualizerDrawUniform2D{}
+        }};
+        GL::Buffer materialUniform{GL::Buffer::TargetHint::Uniform, {
+            MeshVisualizerMaterialUniform{}
+        }};
+        shader
+            .bindTransformationProjectionBuffer(transformationProjectionUniform)
+            .bindDrawBuffer(drawUniform)
+            .bindMaterialBuffer(materialUniform)
+            .draw(circle);
+    } else CORRADE_INTERNAL_ASSERT_UNREACHABLE();
+
+    MAGNUM_VERIFY_NO_GL_ERROR();
+
+    if(!(_manager.loadState("AnyImageImporter") & PluginManager::LoadState::Loaded) ||
+       !(_manager.loadState("TgaImporter") & PluginManager::LoadState::Loaded))
+        CORRADE_SKIP("AnyImageImporter / TgaImporter plugins not found.");
+
+    CORRADE_COMPARE_WITH(
+        /* Dropping the alpha channel, as it's always 1.0 */
+        Containers::arrayCast<Color3ub>(_framebuffer.read(_framebuffer.viewport(), {PixelFormat::RGBA8Unorm}).pixels<Color4ub>()),
+        Utility::Directory::join(_testDir, "MeshVisualizerTestFiles/defaults-objectid2D.tga"),
+        (DebugTools::CompareImageToFile{_manager}));
+}
+
+template<MeshVisualizerGL3D::Flag flag> void MeshVisualizerGLTest::renderDefaultsObjectId3D() {
+    if(flag == MeshVisualizerGL3D::Flag::UniformBuffers) {
+        setTestCaseTemplateName("Flag::UniformBuffers");
+
+        #ifndef MAGNUM_TARGET_GLES
+        if(!GL::Context::current().isExtensionSupported<GL::Extensions::ARB::uniform_buffer_object>())
+            CORRADE_SKIP(GL::Extensions::ARB::uniform_buffer_object::string() << "is not supported.");
+        #endif
+    }
+
+    #ifndef MAGNUM_TARGET_GLES
+    if(!GL::Context::current().isExtensionSupported<GL::Extensions::EXT::gpu_shader4>())
+        CORRADE_SKIP(GL::Extensions::EXT::gpu_shader4::string() << "is not supported.");
+    #endif
+
+    GL::Mesh icosphere = MeshTools::compile(Primitives::icosphereSolid(0));
+
+    MeshVisualizerGL3D shader{MeshVisualizerGL3D::Flag::InstancedObjectId|flag};
+    shader.bindColorMapTexture(_colorMapTexture);
+
+    if(flag == MeshVisualizerGL3D::Flag{}) {
+        shader.draw(icosphere);
+    } else if(flag == MeshVisualizerGL3D::Flag::UniformBuffers) {
+        GL::Buffer projectionUniform{GL::Buffer::TargetHint::Uniform, {
+            ProjectionUniform3D{}
+        }};
+        GL::Buffer transformationUniform{GL::Buffer::TargetHint::Uniform, {
+            TransformationUniform3D{}
+        }};
+        GL::Buffer drawUniform{GL::Buffer::TargetHint::Uniform, {
+            MeshVisualizerDrawUniform3D{}
+        }};
+        GL::Buffer materialUniform{GL::Buffer::TargetHint::Uniform, {
+            MeshVisualizerMaterialUniform{}
+        }};
+        shader
+            .bindProjectionBuffer(projectionUniform)
+            .bindTransformationBuffer(transformationUniform)
+            .bindDrawBuffer(drawUniform)
+            .bindMaterialBuffer(materialUniform)
+            .draw(icosphere);
+    } else CORRADE_INTERNAL_ASSERT_UNREACHABLE();
+
+    MAGNUM_VERIFY_NO_GL_ERROR();
+
+    if(!(_manager.loadState("AnyImageImporter") & PluginManager::LoadState::Loaded) ||
+       !(_manager.loadState("TgaImporter") & PluginManager::LoadState::Loaded))
+        CORRADE_SKIP("AnyImageImporter / TgaImporter plugins not found.");
+
+    CORRADE_COMPARE_WITH(
+        /* Dropping the alpha channel, as it's always 1.0 */
+        Containers::arrayCast<Color3ub>(_framebuffer.read(_framebuffer.viewport(), {PixelFormat::RGBA8Unorm}).pixels<Color4ub>()),
+        Utility::Directory::join(_testDir, "MeshVisualizerTestFiles/defaults-objectid3D.tga"),
+        (DebugTools::CompareImageToFile{_manager}));
+}
+
 template<MeshVisualizerGL2D::Flag flag> void MeshVisualizerGLTest::renderDefaultsInstancedObjectId2D() {
     auto&& data = InstancedObjectIdDefaultsData[testCaseInstanceId()];
     setTestCaseDescription(data.name);
@@ -2710,7 +2886,7 @@ template<MeshVisualizerGL2D::Flag flag> void MeshVisualizerGLTest::renderObjectV
     }
 
     #ifndef MAGNUM_TARGET_GLES
-    if((data.flags2D & MeshVisualizerGL2D::Flag::InstancedObjectId) && !GL::Context::current().isExtensionSupported<GL::Extensions::EXT::gpu_shader4>())
+    if((data.flags2D & MeshVisualizerGL2D::Flag::ObjectId) && !GL::Context::current().isExtensionSupported<GL::Extensions::EXT::gpu_shader4>())
         CORRADE_SKIP(GL::Extensions::EXT::gpu_shader4::string() << "is not supported.");
     #endif
 
@@ -2739,7 +2915,9 @@ template<MeshVisualizerGL2D::Flag flag> void MeshVisualizerGLTest::renderObjectV
 
     Trade::MeshData circleData = Primitives::circle2DSolid(16);
 
-    if(data.flags2D & MeshVisualizerGL2D::Flag::InstancedObjectId) {
+    /* Add the instanced Object ID data even if visualizing just uniform object
+       ID, to test the attribute isn't accidentally accessed always */
+    if(data.flags2D & MeshVisualizerGL2D::Flag::ObjectId) {
         Containers::Array<UnsignedInt> ids{16};
         /* Each two faces share the same ID */
         for(std::size_t i = 0; i != ids.size(); ++i) ids[i] = i/2;
@@ -2777,14 +2955,19 @@ template<MeshVisualizerGL2D::Flag flag> void MeshVisualizerGLTest::renderObjectV
         /* OTOH the wireframe color should stay at full channels, not mixed */
         if(data.flags2D & MeshVisualizerGL2D::Flag::Wireframe)
             shader.setWireframeColor(0xffffff_rgbf);
+        /* For object ID we set a base ID to verify the uniform and instanced
+           ID get summed. */
+        if(data.flags2D & MeshVisualizerGL2D::Flag::ObjectId)
+            shader.setObjectId(8);
         /* For vertex ID we don't want any repeat/wraparound as that causes
            disruptions in the gradient and test failures. There's 17 vertices
            also. */
         if(data.flags2D & MeshVisualizerGL2D::Flag::VertexId)
             shader.setColorMapTransformation(1.0f, -1.0f/17.0f);
         /* For object/primitive ID there's no gradient so a wraparound is okay.
-           This should cover the first half of the colormap, in reverse order;
-           for primitive ID the whole colormap due to the repeat wrapping */
+           For the object ID this should cover the second half of the colormap
+           (due to the uniform object ID), in reverse order; for primitive ID
+           the whole colormap due to the repeat wrapping */
         else
             shader.setColorMapTransformation(0.5f, -1.0f/16.0f);
         shader.draw(circle);
@@ -2796,6 +2979,7 @@ template<MeshVisualizerGL2D::Flag flag> void MeshVisualizerGLTest::renderObjectV
         }};
         GL::Buffer drawUniform{GL::Buffer::TargetHint::Uniform, {
             MeshVisualizerDrawUniform2D{}
+                .setObjectId(8)
         }};
         MeshVisualizerMaterialUniform materialUniformData[1];
         materialUniformData->setColor(0xffff00_rgbf);
@@ -2825,7 +3009,7 @@ template<MeshVisualizerGL2D::Flag flag> void MeshVisualizerGLTest::renderObjectV
         Utility::Directory::join({_testDir, "MeshVisualizerTestFiles", data.file2D}),
         /* AMD has slight off-by-one errors compared to Intel, SwiftShader a
            bit more */
-        (DebugTools::CompareImageToFile{_manager, 4.0f, 0.141f}));
+        (DebugTools::CompareImageToFile{_manager, 4.67f, 0.141f}));
 }
 
 template<MeshVisualizerGL3D::Flag flag> void MeshVisualizerGLTest::renderObjectVertexPrimitiveId3D() {
@@ -2842,7 +3026,7 @@ template<MeshVisualizerGL3D::Flag flag> void MeshVisualizerGLTest::renderObjectV
     }
 
     #ifndef MAGNUM_TARGET_GLES
-    if((data.flags3D & MeshVisualizerGL3D::Flag::InstancedObjectId) && !GL::Context::current().isExtensionSupported<GL::Extensions::EXT::gpu_shader4>())
+    if((data.flags3D & MeshVisualizerGL3D::Flag::ObjectId) && !GL::Context::current().isExtensionSupported<GL::Extensions::EXT::gpu_shader4>())
         CORRADE_SKIP(GL::Extensions::EXT::gpu_shader4::string() << "is not supported.");
     #endif
 
@@ -2871,7 +3055,9 @@ template<MeshVisualizerGL3D::Flag flag> void MeshVisualizerGLTest::renderObjectV
 
     Trade::MeshData icosphereData = Primitives::icosphereSolid(1);
 
-    if(data.flags3D & MeshVisualizerGL3D::Flag::InstancedObjectId) {
+    /* Add the instanced Object ID data even if visualizing just uniform object
+       ID, to test the attribute isn't accidentally accessed always */
+    if(data.flags3D & MeshVisualizerGL3D::Flag::ObjectId) {
         Containers::Array<UnsignedInt> ids{80};
         /* Each four faces share the same ID */
         for(std::size_t i = 0; i != ids.size(); ++i) ids[i] = i/4;
@@ -2908,14 +3094,19 @@ template<MeshVisualizerGL3D::Flag flag> void MeshVisualizerGLTest::renderObjectV
         /* OTOH the wireframe color should stay at full channels, not mixed */
         if(data.flags3D & MeshVisualizerGL3D::Flag::Wireframe)
             shader.setWireframeColor(0xffffff_rgbf);
+        /* For object ID we set a base ID to verify the uniform and instanced
+           ID get summed. */
+        if(data.flags3D & MeshVisualizerGL3D::Flag::ObjectId)
+            shader.setObjectId(20);
         /* For vertex ID we don't want any repeat/wraparound as that causes
            disruptions in the gradient and test failures. There's 42 vertices
            also. */
         if(data.flags3D & MeshVisualizerGL3D::Flag::VertexId)
             shader.setColorMapTransformation(1.0f, -1.0f/42.0f);
         /* For object/primitive ID there's no gradient so a wraparound is okay.
-           This should cover the first half of the colormap, in reverse order;
-           for primitive ID the whole colormap due to the repeat wrapping */
+           For the object ID this should cover the second half of the colormap
+           (due to the uniform object ID), in reverse order; for primitive ID
+           the whole colormap due to the repeat wrapping */
         else
             shader.setColorMapTransformation(0.5f, -1.0f/40.0f);
         shader.draw(icosphere);
@@ -2935,6 +3126,7 @@ template<MeshVisualizerGL3D::Flag flag> void MeshVisualizerGLTest::renderObjectV
         }};
         GL::Buffer drawUniform{GL::Buffer::TargetHint::Uniform, {
             MeshVisualizerDrawUniform3D{}
+                .setObjectId(20)
         }};
         MeshVisualizerMaterialUniform materialUniformData[1];
         materialUniformData->setColor(0xffff00_rgbf);
diff --git a/src/Magnum/Shaders/Test/MeshVisualizerGL_Test.cpp b/src/Magnum/Shaders/Test/MeshVisualizerGL_Test.cpp
index 10e7ffc53..f13e7a11b 100644
--- a/src/Magnum/Shaders/Test/MeshVisualizerGL_Test.cpp
+++ b/src/Magnum/Shaders/Test/MeshVisualizerGL_Test.cpp
@@ -152,17 +152,37 @@ void MeshVisualizerGL_Test::debugFlags3D() {
 
 #ifndef MAGNUM_TARGET_GLES2
 void MeshVisualizerGL_Test::debugFlagsSupersets2D() {
+    /* InstancedObjectId is a superset of ObjectId so only one should be
+       printed */
+    {
+        std::ostringstream out;
+        Debug{&out} << (MeshVisualizerGL2D::Flag::InstancedObjectId|MeshVisualizerGL2D::Flag::ObjectId);
+        CORRADE_COMPARE(out.str(), "Shaders::MeshVisualizerGL2D::Flag::InstancedObjectId\n");
+    }
+
     /* MultiDraw is a superset of UniformBuffers so only one should be printed */
-    std::ostringstream out;
-    Debug{&out} << (MeshVisualizerGL2D::Flag::MultiDraw|MeshVisualizerGL2D::Flag::UniformBuffers);
-    CORRADE_COMPARE(out.str(), "Shaders::MeshVisualizerGL2D::Flag::MultiDraw\n");
+    {
+        std::ostringstream out;
+        Debug{&out} << (MeshVisualizerGL2D::Flag::MultiDraw|MeshVisualizerGL2D::Flag::UniformBuffers);
+        CORRADE_COMPARE(out.str(), "Shaders::MeshVisualizerGL2D::Flag::MultiDraw\n");
+    }
 }
 
 void MeshVisualizerGL_Test::debugFlagsSupersets3D() {
+    /* InstancedObjectId is a superset of ObjectId so only one should be
+       printed */
+    {
+        std::ostringstream out;
+        Debug{&out} << (MeshVisualizerGL3D::Flag::InstancedObjectId|MeshVisualizerGL3D::Flag::ObjectId);
+        CORRADE_COMPARE(out.str(), "Shaders::MeshVisualizerGL3D::Flag::InstancedObjectId\n");
+    }
+
     /* MultiDraw is a superset of UniformBuffers so only one should be printed */
-    std::ostringstream out;
-    Debug{&out} << (MeshVisualizerGL3D::Flag::MultiDraw|MeshVisualizerGL3D::Flag::UniformBuffers);
-    CORRADE_COMPARE(out.str(), "Shaders::MeshVisualizerGL3D::Flag::MultiDraw\n");
+    {
+        std::ostringstream out;
+        Debug{&out} << (MeshVisualizerGL3D::Flag::MultiDraw|MeshVisualizerGL3D::Flag::UniformBuffers);
+        CORRADE_COMPARE(out.str(), "Shaders::MeshVisualizerGL3D::Flag::MultiDraw\n");
+    }
 }
 #endif
 
diff --git a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/defaults-objectid2D.tga b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/defaults-objectid2D.tga
new file mode 100644
index 000000000..b8d999b78
Binary files /dev/null and b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/defaults-objectid2D.tga differ
diff --git a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/defaults-objectid3D.tga b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/defaults-objectid3D.tga
new file mode 100644
index 000000000..b4caf06d4
Binary files /dev/null and b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/defaults-objectid3D.tga differ
diff --git a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/instancedobjectid2D.tga b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/instancedobjectid2D.tga
index 6e6a7b4af..c31502283 100644
Binary files a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/instancedobjectid2D.tga and b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/instancedobjectid2D.tga differ
diff --git a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/instancedobjectid3D.tga b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/instancedobjectid3D.tga
index 90e05699e..8c4e19df2 100644
Binary files a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/instancedobjectid3D.tga and b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/instancedobjectid3D.tga differ
diff --git a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/objectid2D.tga b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/objectid2D.tga
new file mode 100644
index 000000000..bd42fbbed
Binary files /dev/null and b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/objectid2D.tga differ
diff --git a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/objectid3D.tga b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/objectid3D.tga
new file mode 100644
index 000000000..81654345a
Binary files /dev/null and b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/objectid3D.tga differ
diff --git a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/wireframe-instancedobjectid2D.tga b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/wireframe-instancedobjectid2D.tga
index 5ed8df360..0a64e6270 100644
Binary files a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/wireframe-instancedobjectid2D.tga and b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/wireframe-instancedobjectid2D.tga differ
diff --git a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/wireframe-instancedobjectid3D.tga b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/wireframe-instancedobjectid3D.tga
index 44a7028c9..13b87c990 100644
Binary files a/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/wireframe-instancedobjectid3D.tga and b/src/Magnum/Shaders/Test/MeshVisualizerTestFiles/wireframe-instancedobjectid3D.tga differ
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