diff --git a/src/Magnum/Shaders/FlatGL.h b/src/Magnum/Shaders/FlatGL.h
index a7353d067..dc9aa7a63 100644
--- a/src/Magnum/Shaders/FlatGL.h
+++ b/src/Magnum/Shaders/FlatGL.h
@@ -131,8 +131,11 @@ If you have a batch of meshes with different object IDs, enable
 attribute. The output will contain a sum of the per-vertex ID and ID coming
 from @ref setObjectId().
 
-@requires_gles30 Object ID output requires integer buffer attachments, which
-    are not available in OpenGL ES 2.0 or WebGL 1.0.
+@requires_gl30 Extension @gl_extension{EXT,texture_integer}
+@requires_gles30 Object ID output requires integer support in shaders, which
+    is not available in OpenGL ES 2.0.
+@requires_webgl20 Object ID output requires integer support in shaders, which
+    is not available in WebGL 1.0.
 
 @section Shaders-FlatGL-instancing Instanced rendering
 
@@ -242,7 +245,9 @@ template<UnsignedInt dimensions> class MAGNUM_SHADERS_EXPORT FlatGL: public GL::
          * Used only if @ref Flag::InstancedObjectId is set.
          * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
          * @requires_gles30 Object ID output requires integer support in
-         *      shaders, which is not available in OpenGL ES 2.0 or WebGL 1.0.
+         *      shaders, which is not available in OpenGL ES 2.0.
+         * @requires_webgl20 Object ID output requires integer support in
+         *      shaders, which is not available in WebGL 1.0.
          */
         typedef typename GenericGL<dimensions>::ObjectId ObjectId;
         #endif
@@ -314,8 +319,9 @@ template<UnsignedInt dimensions> class MAGNUM_SHADERS_EXPORT FlatGL: public GL::
              * @ref Shaders-FlatGL-object-id for more information.
              * @requires_gl30 Extension @gl_extension{EXT,texture_integer}
              * @requires_gles30 Object ID output requires integer support in
-             *      shaders, which is not available in OpenGL ES 2.0 or WebGL
-             *      1.0.
+             *      shaders, which is not available in OpenGL ES 2.0.
+             * @requires_webgl20 Object ID output requires integer support in
+             *      shaders, which is not available in WebGL 1.0.
              * @m_since{2019,10}
              */
             ObjectIdOutput = GenericGL<dimensions>::ObjectIdOutput
@@ -369,8 +375,9 @@ template<UnsignedInt dimensions> class MAGNUM_SHADERS_EXPORT FlatGL: public GL::
              * more information.
              * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
              * @requires_gles30 Object ID output requires integer support in
-             *      shaders, which is not available in OpenGL ES 2.0 or WebGL
-             *      1.0.
+             *      shaders, which is not available in OpenGL ES 2.0.
+             * @requires_webgl20 Object ID output requires integer support in
+             *      shaders, which is not available in WebGL 1.0.
              * @m_since{2019,10}
              */
             ObjectId = 1 << 4,
@@ -384,8 +391,9 @@ template<UnsignedInt dimensions> class MAGNUM_SHADERS_EXPORT FlatGL: public GL::
              * information.
              * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
              * @requires_gles30 Object ID output requires integer support in
-             *      shaders, which is not available in OpenGL ES 2.0 or WebGL
-             *      1.0.
+             *      shaders, which is not available in OpenGL ES 2.0.
+             * @requires_webgl20 Object ID output requires integer support in
+             *      shaders, which is not available in WebGL 1.0.
              * @m_since{2020,06}
              */
             InstancedObjectId = (1 << 5)|ObjectId,
@@ -728,7 +736,9 @@ template<UnsignedInt dimensions> class MAGNUM_SHADERS_EXPORT FlatGL: public GL::
          * instead.
          * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
          * @requires_gles30 Object ID output requires integer support in
-         *      shaders, which is not available in OpenGL ES 2.0 or WebGL 1.0.
+         *      shaders, which is not available in OpenGL ES 2.0.
+         * @requires_webgl20 Object ID output requires integer support in
+         *      shaders, which is not available in WebGL 1.0.
          */
         FlatGL<dimensions>& setObjectId(UnsignedInt id);
         #endif
diff --git a/src/Magnum/Shaders/GenericGL.h b/src/Magnum/Shaders/GenericGL.h
index eb748f994..4e0293e98 100644
--- a/src/Magnum/Shaders/GenericGL.h
+++ b/src/Magnum/Shaders/GenericGL.h
@@ -269,7 +269,9 @@ template<UnsignedInt dimensions> struct GenericGL {
          * integral attachment.
          * @requires_gl30 Extension @gl_extension{EXT,texture_integer}
          * @requires_gles30 Object ID output requires integer support in
-         *      shaders, which is not available in OpenGL ES 2.0 or WebGL 1.0.
+         *      shaders, which is not available in OpenGL ES 2.0.
+         * @requires_webgl20 Object ID output requires integer support in
+         *      shaders, which is not available in WebGL 1.0.
          */
         ObjectIdOutput = 1
         #endif
@@ -361,7 +363,9 @@ template<UnsignedInt dimensions> struct GenericGL {
      * @ref Tangent4 instead.
      * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
      * @requires_gles30 Object ID output requires integer support in shaders,
-     *      which is not available in OpenGL ES 2.0 or WebGL 1.0.
+     *      which is not available in OpenGL ES 2.0.
+     * @requires_webgl20 Object ID output requires integer support in shaders,
+     *      which is not available in WebGL 1.0.
      */
     typedef GL::Attribute<4, UnsignedInt> ObjectId;
     #endif
diff --git a/src/Magnum/Shaders/MeshVisualizerGL.h b/src/Magnum/Shaders/MeshVisualizerGL.h
index c066e2165..0a9e5e7c4 100644
--- a/src/Magnum/Shaders/MeshVisualizerGL.h
+++ b/src/Magnum/Shaders/MeshVisualizerGL.h
@@ -167,7 +167,9 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGL2D: public Implementation::MeshVisua
          * Used only if @ref Flag::InstancedObjectId is set.
          * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
          * @requires_gles30 Object ID output requires integer support in
-         *      shaders, which is not available in OpenGL ES 2.0 or WebGL 1.0.
+         *      shaders, which is not available in OpenGL ES 2.0.
+         * @requires_webgl20 Object ID output requires integer support in
+         *      shaders, which is not available in WebGL 1.0.
          */
         typedef GenericGL3D::ObjectId ObjectId;
         #endif
@@ -783,15 +785,20 @@ triangle mesh. You can use @ref MeshTools::duplicate() (and potentially
 @ref MeshTools::generateIndices()) to conveniently convert the mesh to a
 non-indexed @ref MeshPrimitive::Triangles.
 
-@requires_gl32 The `gl_PrimitiveID` shader variable is not available on OpenGL
-    3.1 and lower.
+@requires_gl30 Extension @gl_extension{EXT,gpu_shader4} for object ID input
 @requires_gl30 The `gl_VertexID` shader variable is not available on OpenGL
     2.1.
+@requires_gl32 The `gl_PrimitiveID` shader variable is not available on OpenGL
+    3.1 and lower.
 @requires_gles32 The `gl_PrimitiveID` shader variable is not available on
     OpenGL ES 3.1 and lower.
+@requires_gles30 Object ID input requires integer support in shaders, which
+    is not available in OpenGL ES 2.0.
 @requires_gles30 The `gl_VertexID` shader variable is not available on OpenGL
     ES 2.0.
 @requires_gles `gl_PrimitiveID` is not available in WebGL.
+@requires_webgl20 Object ID input requires integer support in shaders, which
+    is not available in WebGL 1.0.
 @requires_webgl20 `gl_VertexID` is not available in WebGL 1.0.
 
 @section Shaders-MeshVisualizerGL3D-ubo Uniform buffers
@@ -906,7 +913,9 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGL3D: public Implementation::MeshVisua
          * Used only if @ref Flag::InstancedObjectId is set.
          * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
          * @requires_gles30 Object ID output requires integer support in
-         *      shaders, which is not available in OpenGL ES 2.0 or WebGL 1.0.
+         *      shaders, which is not available in OpenGL ES 2.0.
+         * @requires_webgl20 Object ID output requires integer support in
+         *      shaders, which is not available in WebGL 1.0.
          */
         typedef GenericGL3D::ObjectId ObjectId;
         #endif
@@ -956,8 +965,9 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizerGL3D: public Implementation::MeshVisua
              * @ref Flag::VertexId and @ref Flag::PrimitiveId.
              * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
              * @requires_gles30 Object ID output requires integer support in
-             *      shaders, which is not available in OpenGL ES 2.0 or WebGL
-             *      1.0.
+             *      shaders, which is not available in OpenGL ES 2.0.
+             * @requires_webgl20 Object ID output requires integer support in
+             *      shaders, which is not available in WebGL 1.0.
              * @m_since{2020,06}
              */
             InstancedObjectId = 1 << 2,
diff --git a/src/Magnum/Shaders/PhongGL.h b/src/Magnum/Shaders/PhongGL.h
index 754d34cc3..93667bcbc 100644
--- a/src/Magnum/Shaders/PhongGL.h
+++ b/src/Magnum/Shaders/PhongGL.h
@@ -221,8 +221,11 @@ The functionality is practically the same as in the @ref FlatGL shader, see
 @ref Shaders-FlatGL-object-id "its documentation" for more information and usage
 example.
 
-@requires_gles30 Object ID output requires integer buffer attachments, which
-    are not available in OpenGL ES 2.0 or WebGL 1.0.
+@requires_gl30 Extension @gl_extension{EXT,texture_integer}
+@requires_gles30 Object ID output requires integer support in shaders, which
+    is not available in OpenGL ES 2.0.
+@requires_webgl20 Object ID output requires integer support in shaders, which
+    is not available in WebGL 1.0.
 
 @section Shaders-PhongGL-instancing Instanced rendering
 
@@ -385,7 +388,9 @@ class MAGNUM_SHADERS_EXPORT PhongGL: public GL::AbstractShaderProgram {
          * Used only if @ref Flag::InstancedObjectId is set.
          * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
          * @requires_gles30 Object ID output requires integer support in
-         *      shaders, which is not available in OpenGL ES 2.0 or WebGL 1.0.
+         *      shaders, which is not available in OpenGL ES 2.0.
+         * @requires_webgl20 Object ID output requires integer support in
+         *      shaders, which is not available in WebGL 1.0.
          */
         typedef GenericGL3D::ObjectId ObjectId;
         #endif
@@ -471,8 +476,9 @@ class MAGNUM_SHADERS_EXPORT PhongGL: public GL::AbstractShaderProgram {
              * @ref Shaders-PhongGL-object-id for more information.
              * @requires_gl30 Extension @gl_extension{EXT,texture_integer}
              * @requires_gles30 Object ID output requires integer support in
-             *      shaders, which is not available in OpenGL ES 2.0 or WebGL
-             *      1.0.
+             *      shaders, which is not available in OpenGL ES 2.0.
+             * @requires_webgl20 Object ID output requires integer support in
+             *      shaders, which is not available in WebGL 1.0.
              * @m_since{2019,10}
              */
             ObjectIdOutput = GenericGL3D::ObjectIdOutput
@@ -557,8 +563,9 @@ class MAGNUM_SHADERS_EXPORT PhongGL: public GL::AbstractShaderProgram {
              * for more information.
              * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
              * @requires_gles30 Object ID output requires integer support in
-             *      shaders, which is not available in OpenGL ES 2.0 or WebGL
-             *      1.0.
+             *      shaders, which is not available in OpenGL ES 2.0.
+             * @requires_webgl20 Object ID output requires integer support in
+             *      shaders, which is not available in WebGL 1.0.
              * @m_since{2019,10}
              */
             ObjectId = 1 << 7,
@@ -572,8 +579,9 @@ class MAGNUM_SHADERS_EXPORT PhongGL: public GL::AbstractShaderProgram {
              * information.
              * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
              * @requires_gles30 Object ID output requires integer support in
-             *      shaders, which is not available in OpenGL ES 2.0 or WebGL
-             *      1.0.
+             *      shaders, which is not available in OpenGL ES 2.0.
+             * @requires_webgl20 Object ID output requires integer support in
+             *      shaders, which is not available in WebGL 1.0.
              * @m_since{2020,06}
              */
             InstancedObjectId = (1 << 8)|ObjectId,
@@ -976,7 +984,9 @@ class MAGNUM_SHADERS_EXPORT PhongGL: public GL::AbstractShaderProgram {
          * instead.
          * @requires_gl30 Extension @gl_extension{EXT,gpu_shader4}
          * @requires_gles30 Object ID output requires integer support in
-         *      shaders, which is not available in OpenGL ES 2.0 or WebGL 1.0.
+         *      shaders, which is not available in OpenGL ES 2.0.
+         * @requires_webgl20 Object ID output requires integer support in
+         *      shaders, which is not available in WebGL 1.0.
          */
         PhongGL& setObjectId(UnsignedInt id);
         #endif