diff --git a/src/Magnum/Shaders/Flat.frag b/src/Magnum/Shaders/Flat.frag
index 623216fe7..15cf8d1fe 100644
--- a/src/Magnum/Shaders/Flat.frag
+++ b/src/Magnum/Shaders/Flat.frag
@@ -23,6 +23,10 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+#if defined(OBJECT_ID) && !defined(GL_ES) && !defined(NEW_GLSL)
+#extension GL_EXT_gpu_shader4: require
+#endif
+
 #ifndef NEW_GLSL
 #define fragmentColor gl_FragColor
 #define texture texture2D
diff --git a/src/Magnum/Shaders/Flat.h b/src/Magnum/Shaders/Flat.h
index 9489b698f..15f79816c 100644
--- a/src/Magnum/Shaders/Flat.h
+++ b/src/Magnum/Shaders/Flat.h
@@ -198,9 +198,9 @@ template<UnsignedInt dimensions> class MAGNUM_SHADERS_EXPORT Flat: public GL::Ab
          *
          * @ref shaders-generic "Generic attribute", @ref Magnum::UnsignedInt.
          * Used only if @ref Flag::InstancedObjectId is set.
-         * @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,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.
          */
         typedef typename Generic<dimensions>::ObjectId ObjectId;
         #endif
@@ -251,9 +251,10 @@ template<UnsignedInt dimensions> class MAGNUM_SHADERS_EXPORT Flat: public GL::Ab
              * single-component unsigned integral attachment. Writes the value
              * set in @ref setObjectId() there, see
              * @ref Shaders-Phong-object-id for more information.
-             * @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 or WebGL
+             *      1.0.
              * @m_since{2019,10}
              */
             ObjectIdOutput = Generic<dimensions>::ObjectIdOutput
@@ -305,9 +306,10 @@ template<UnsignedInt dimensions> class MAGNUM_SHADERS_EXPORT Flat: public GL::Ab
             /**
              * Enable object ID output. See @ref Shaders-Flat-object-id for
              * more information.
-             * @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,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.
              * @m_since{2019,10}
              */
             ObjectId = 1 << 4,
@@ -318,9 +320,10 @@ template<UnsignedInt dimensions> class MAGNUM_SHADERS_EXPORT Flat: public GL::Ab
              * the per-vertex ID and ID coming from @ref setObjectId().
              * Implicitly enables @ref Flag::ObjectId. See
              * @ref Shaders-Flat-object-id for more information.
-             * @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,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.
              * @m_since_latest
              */
             InstancedObjectId = (1 << 5)|ObjectId,
@@ -473,9 +476,9 @@ template<UnsignedInt dimensions> class MAGNUM_SHADERS_EXPORT Flat: public GL::Ab
          * @ref Shaders-Flat-object-id for more information. Default is
          * @cpp 0 @ce. If @ref Flag::InstancedObjectId is enabled as well, this
          * value is combined with ID coming from the @ref ObjectId attribute.
-         * @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,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.
          */
         Flat<dimensions>& setObjectId(UnsignedInt id);
         #endif
diff --git a/src/Magnum/Shaders/Flat.vert b/src/Magnum/Shaders/Flat.vert
index 08bf36814..a89d2bb61 100644
--- a/src/Magnum/Shaders/Flat.vert
+++ b/src/Magnum/Shaders/Flat.vert
@@ -23,6 +23,10 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+#if defined(INSTANCED_OBJECT_ID) && !defined(GL_ES) && !defined(NEW_GLSL)
+#extension GL_EXT_gpu_shader4: require
+#endif
+
 #ifndef NEW_GLSL
 #define in attribute
 #define out varying
diff --git a/src/Magnum/Shaders/Generic.h b/src/Magnum/Shaders/Generic.h
index cb1e9f9a1..43858c0cd 100644
--- a/src/Magnum/Shaders/Generic.h
+++ b/src/Magnum/Shaders/Generic.h
@@ -247,9 +247,9 @@ template<UnsignedInt dimensions> struct Generic {
         /**
          * Object ID shader output. Expects a single-component unsigned
          * integral attachment.
-         * @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 or WebGL 1.0.
          */
         ObjectIdOutput = 1
         #endif
@@ -339,9 +339,9 @@ template<UnsignedInt dimensions> struct Generic {
      * This attribute conflicts with @ref Bitangent, if you want to use both
      * instanced object ID and bitangents, you need to reconstruct them from
      * @ref Tangent4 instead.
-     *
-     * @requires_gles30 Object ID output requires integer attributes, which are
-     *      not available in OpenGL ES 2.0 or WebGL 1.0.
+     * @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.
      */
     typedef GL::Attribute<4, UnsignedInt> ObjectId;
     #endif
diff --git a/src/Magnum/Shaders/MeshVisualizer.h b/src/Magnum/Shaders/MeshVisualizer.h
index c2cfee7d0..bd4cffad0 100644
--- a/src/Magnum/Shaders/MeshVisualizer.h
+++ b/src/Magnum/Shaders/MeshVisualizer.h
@@ -145,10 +145,9 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizer2D: public Implementation::MeshVisuali
          *
          * @ref shaders-generic "Generic attribute", @ref Magnum::UnsignedInt.
          * Used only if @ref Flag::InstancedObjectId is set.
-         * @requires_gles30 Object ID input requires integer attributes, which
-         *      are not available in OpenGL ES 2.0.
-         * @requires_webgl20 Object ID input requires integer attributes, which
-         *      are not available in WebGL 1.0.
+         * @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.
          */
         typedef Generic3D::ObjectId ObjectId;
         #endif
@@ -558,10 +557,9 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizer3D: public Implementation::MeshVisuali
          *
          * @ref shaders-generic "Generic attribute", @ref Magnum::UnsignedInt.
          * Used only if @ref Flag::InstancedObjectId is set.
-         * @requires_gles30 Object ID input requires integer attributes, which
-         *      are not available in OpenGL ES 2.0.
-         * @requires_webgl20 Object ID input requires integer attributes, which
-         *      are not available in WebGL 1.0.
+         * @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.
          */
         typedef Generic3D::ObjectId ObjectId;
         #endif
@@ -609,8 +607,10 @@ class MAGNUM_SHADERS_EXPORT MeshVisualizer3D: public Implementation::MeshVisuali
              * Visualize instanced object ID. You need to provide the
              * @ref ObjectId attribute in the mesh. Mutually exclusive with
              * @ref Flag::PrimitiveId.
-             * @requires_gles30 Object ID input requires integer attributes,
-             *      which are not available in OpenGL ES 2.0 or WebGL 1.0.
+             * @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.
              * @m_since_latest
              */
             InstancedObjectId = 1 << 2,
diff --git a/src/Magnum/Shaders/MeshVisualizer.vert b/src/Magnum/Shaders/MeshVisualizer.vert
index 11108f30f..e8ff213e6 100644
--- a/src/Magnum/Shaders/MeshVisualizer.vert
+++ b/src/Magnum/Shaders/MeshVisualizer.vert
@@ -23,6 +23,10 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+#if defined(INSTANCED_OBJECT_ID) && !defined(GL_ES) && !defined(NEW_GLSL)
+#extension GL_EXT_gpu_shader4: require
+#endif
+
 #ifndef NEW_GLSL
 #define in attribute
 #define out varying
diff --git a/src/Magnum/Shaders/Phong.frag b/src/Magnum/Shaders/Phong.frag
index 034fbee25..47f739be2 100644
--- a/src/Magnum/Shaders/Phong.frag
+++ b/src/Magnum/Shaders/Phong.frag
@@ -23,6 +23,10 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+#if defined(OBJECT_ID) && !defined(GL_ES) && !defined(NEW_GLSL)
+#extension GL_EXT_gpu_shader4: require
+#endif
+
 #ifndef NEW_GLSL
 #define in varying
 #define fragmentColor gl_FragColor
diff --git a/src/Magnum/Shaders/Phong.h b/src/Magnum/Shaders/Phong.h
index 234328cda..fc75fddb0 100644
--- a/src/Magnum/Shaders/Phong.h
+++ b/src/Magnum/Shaders/Phong.h
@@ -214,9 +214,9 @@ class MAGNUM_SHADERS_EXPORT Phong: public GL::AbstractShaderProgram {
          *
          * @ref shaders-generic "Generic attribute", @ref Magnum::UnsignedInt.
          * Used only if @ref Flag::InstancedObjectId is set.
-         * @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,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.
          */
         typedef Generic3D::ObjectId ObjectId;
         #endif
@@ -282,9 +282,10 @@ class MAGNUM_SHADERS_EXPORT Phong: public GL::AbstractShaderProgram {
              * single-component unsigned integral attachment. Writes the value
              * set in @ref setObjectId() there, see
              * @ref Shaders-Phong-object-id for more information.
-             * @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 or WebGL
+             *      1.0.
              * @m_since{2019,10}
              */
             ObjectIdOutput = Generic3D::ObjectIdOutput
@@ -357,9 +358,10 @@ class MAGNUM_SHADERS_EXPORT Phong: public GL::AbstractShaderProgram {
             /**
              * Enable object ID output. See @ref Shaders-Phong-object-id
              * for more information.
-             * @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,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.
              * @m_since{2019,10}
              */
             ObjectId = 1 << 7,
@@ -370,9 +372,10 @@ class MAGNUM_SHADERS_EXPORT Phong: public GL::AbstractShaderProgram {
              * the per-vertex ID and ID coming from @ref setObjectId().
              * Implicitly enables @ref Flag::ObjectId. See
              * @ref Shaders-Phong-object-id for more information.
-             * @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,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.
              * @m_since_latest
              */
             InstancedObjectId = (1 << 8)|ObjectId,
@@ -593,9 +596,9 @@ class MAGNUM_SHADERS_EXPORT Phong: public GL::AbstractShaderProgram {
          * enabled. Value set here is written to the @ref ObjectIdOutput, see
          * @ref Shaders-Phong-object-id for more information. Default is
          * @cpp 0 @ce.
-         * @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,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.
          */
         Phong& setObjectId(UnsignedInt id);
         #endif
diff --git a/src/Magnum/Shaders/Phong.vert b/src/Magnum/Shaders/Phong.vert
index 2868f706d..e13c75176 100644
--- a/src/Magnum/Shaders/Phong.vert
+++ b/src/Magnum/Shaders/Phong.vert
@@ -23,6 +23,10 @@
     DEALINGS IN THE SOFTWARE.
 */
 
+#if defined(INSTANCED_OBJECT_ID) && !defined(GL_ES) && !defined(NEW_GLSL)
+#extension GL_EXT_gpu_shader4: require
+#endif
+
 #ifndef NEW_GLSL
 #define in attribute
 #define out varying