diff --git a/doc/opengl-support.dox b/doc/opengl-support.dox
index c6c07001d..be3879ab4 100644
--- a/doc/opengl-support.dox
+++ b/doc/opengl-support.dox
@@ -524,7 +524,6 @@ namespace on @ref MAGNUM_TARGET_GLES2 "WebGL 2.0 builds".
 Extension                                   | Status
 ------------------------------------------- | ------
 @webgl_extension{ANGLE,instanced_arrays}    | done
-@webgl_extension{EXT,color_buffer_half_float} | |
 @webgl_extension{EXT,frag_depth}            | done (shading language only)
 @webgl_extension{EXT,sRGB}                  | done
 @webgl_extension{EXT,blend_minmax}          | done
@@ -553,6 +552,7 @@ Extension                                   | Status
 Extension                                   | Status
 ------------------------------------------- | ------
 @webgl_extension{EXT,texture_filter_anisotropic} | done
+@webgl_extension{EXT,color_buffer_half_float} | |
 @webgl_extension{EXT,disjoint_timer_query}  | only time elapsed query
 @webgl_extension{EXT,disjoint_timer_query_webgl2}  | [missing support in Emscripten](https://github.com/emscripten-core/emscripten/pull/9652)
 @webgl_extension{EXT,color_buffer_float}    | |
diff --git a/src/Magnum/GL/Context.cpp b/src/Magnum/GL/Context.cpp
index 1915328dc..b15b5a0fd 100644
--- a/src/Magnum/GL/Context.cpp
+++ b/src/Magnum/GL/Context.cpp
@@ -271,6 +271,7 @@ constexpr Extension ExtensionList[]{
     #ifndef MAGNUM_TARGET_GLES2
     Extensions::EXT::color_buffer_float{},
     #endif
+    Extensions::EXT::color_buffer_half_float{},
     #ifdef MAGNUM_TARGET_GLES2
     Extensions::EXT::disjoint_timer_query{},
     #endif
@@ -311,7 +312,6 @@ constexpr Extension ExtensionListES300[]{
     #ifdef MAGNUM_TARGET_GLES2
     Extensions::ANGLE::instanced_arrays{},
     Extensions::EXT::blend_minmax{},
-    Extensions::EXT::color_buffer_half_float{},
     Extensions::EXT::frag_depth{},
     Extensions::EXT::sRGB{},
     Extensions::EXT::shader_texture_lod{},
diff --git a/src/Magnum/GL/Extensions.h b/src/Magnum/GL/Extensions.h
index 31f9b4cf4..9c2750da1 100644
--- a/src/Magnum/GL/Extensions.h
+++ b/src/Magnum/GL/Extensions.h
@@ -275,9 +275,7 @@ namespace ANGLE {
     #endif
 } namespace EXT {
     _extension( 2,EXT,texture_filter_anisotropic,   GLES200,    None) // #11
-    #ifdef MAGNUM_TARGET_GLES2
     _extension( 3,EXT,color_buffer_half_float,      GLES200,    None) // #14
-    #endif
     #ifdef MAGNUM_TARGET_GLES2
     _extension( 4,EXT,frag_depth,                   GLES200, GLES300) // #16
     _extension( 5,EXT,sRGB,                         GLES200, GLES300) // #17
diff --git a/src/Magnum/GL/PixelFormat.h b/src/Magnum/GL/PixelFormat.h
index 7700ebd62..11902026b 100644
--- a/src/Magnum/GL/PixelFormat.h
+++ b/src/Magnum/GL/PixelFormat.h
@@ -433,8 +433,10 @@ enum class PixelType: GLenum {
      *      use for texture reading in WebGL 1.0.
      * @requires_webgl20 Extension @webgl_extension{OES,texture_half_float_linear}
      *      for filtering the texture using @ref SamplerFilter::Linear.
-     * @requires_webgl_extension Extension @webgl_extension{EXT,color_buffer_half_float}
-     *      to use the texture as a render target.
+     * @requires_webgl_extension Extension
+     *      @webgl_extension{EXT,color_buffer_half_float} in WebGL 1.0 and 2.0
+     *      or @webgl_extension{EXT,color_buffer_float} in WebGL 2.0 to use the
+     *      texture as a render target.
      */
     #ifndef MAGNUM_TARGET_GLES2
     Half = GL_HALF_FLOAT,
@@ -462,9 +464,10 @@ enum class PixelType: GLenum {
      *      for texture reading in WebGL 1.0.
      * @requires_webgl_extension Extension @webgl_extension{OES,texture_float_linear}
      *      for filtering the texture using @ref SamplerFilter::Linear.
-     * @requires_webgl_extension Extension @webgl_extension{WEBGL,color_buffer_float}
-     *      in WebGL 1.0 or @webgl_extension{EXT,color_buffer_float} in WebGL
-     *      2.0 to use the texture as a render target.
+     * @requires_webgl_extension Extension
+     *      @webgl_extension{WEBGL,color_buffer_float} in WebGL 1.0 or
+     *      @webgl_extension{EXT,color_buffer_float} in WebGL 2.0 to use the
+     *      texture as a render target.
      */
     Float = GL_FLOAT,
 
@@ -593,6 +596,8 @@ enum class PixelType: GLenum {
      * @requires_gles30 Only 8bit and 16bit types are available in OpenGL ES
      *      2.0.
      * @requires_webgl20 Only 8bit and 16bit types are available in WebGL 1.0.
+     * @requires_webgl_extension @webgl_extension{EXT,color_buffer_float} in
+     *      WebGL 2.0 to use the texture as a render target.
      */
     UnsignedInt5999Rev = GL_UNSIGNED_INT_5_9_9_9_REV,
     #endif
diff --git a/src/Magnum/GL/RenderbufferFormat.h b/src/Magnum/GL/RenderbufferFormat.h
index 0a0a3182a..b6d0ec9d8 100644
--- a/src/Magnum/GL/RenderbufferFormat.h
+++ b/src/Magnum/GL/RenderbufferFormat.h
@@ -408,9 +408,11 @@ enum class RenderbufferFormat: GLenum {
      * @requires_webgl20 Not defined in WebGL 1.0 builds. Only four-component
      *      half-float formats can be ised as a render target in WebGL 1.0, see
      *      @ref RenderbufferFormat::RGBA16F for more information.
-     * @requires_webgl_extension Extension @webgl_extension{EXT,color_buffer_float}
-     *      in WebGL 2.0. Use @ref RenderbufferFormat::R16UI or
-     *      @ref RenderbufferFormat::R16I instead if not available.
+     * @requires_webgl_extension Extension
+     *      @webgl_extension{EXT,color_buffer_half_float} or
+     *      @webgl_extension{EXT,color_buffer_float} in WebGL 2.0. Use
+     *      @ref RenderbufferFormat::R16UI or @ref RenderbufferFormat::R16I
+     *      instead if not available.
      */
     #ifndef MAGNUM_TARGET_GLES2
     R16F = GL_R16F,
@@ -427,9 +429,11 @@ enum class RenderbufferFormat: GLenum {
      * @requires_webgl20 Not defined in WebGL 1.0 builds. Only four-component
      *      half-float formats can be ised as a render target in WebGL 1.0, see
      *      @ref RenderbufferFormat::RGBA16F for more information.
-     * @requires_webgl_extension Extension @webgl_extension{EXT,color_buffer_float}
-     *      in WebGL 2.0. Use @ref RenderbufferFormat::RG16UI or
-     *      @ref RenderbufferFormat::RG16I instead if not available.
+     * @requires_webgl_extension Extension
+     *      @webgl_extension{EXT,color_buffer_half_float} or
+     *      @webgl_extension{EXT,color_buffer_float} in WebGL 2.0. Use
+     *      @ref RenderbufferFormat::RG16UI or @ref RenderbufferFormat::RG16I
+     *      instead if not available.
      */
     #ifndef MAGNUM_TARGET_GLES2
     RG16F = GL_RG16F,
@@ -444,10 +448,11 @@ enum class RenderbufferFormat: GLenum {
      * @requires_gles32 Extension @gl_extension{EXT,color_buffer_half_float}. Use
      *      @ref RenderbufferFormat::RGBA16UI or @ref RenderbufferFormat::RGBA16I
      *      instead if not available.
-     * @requires_webgl_extension Extension @webgl_extension{EXT,color_buffer_half_float}
-     *      in WebGL 1.0, @webgl_extension{EXT,color_buffer_half_float} in
-     *      WebGL 2.0. Use @ref RenderbufferFormat::RGBA16UI or
-     *      @ref RenderbufferFormat::RGBA16I instead if not available.
+     * @requires_webgl_extension Extension
+     *      @webgl_extension{EXT,color_buffer_half_float} in WebGL 1.0 and 2.0
+     *      or @webgl_extension{EXT,color_buffer_float} in WebGL 2.0. Use
+     *      @ref RenderbufferFormat::RGBA16UI or @ref RenderbufferFormat::RGBA16I
+     *      instead if not available.
      */
     #ifndef MAGNUM_TARGET_GLES2
     RGBA16F = GL_RGBA16F,
diff --git a/src/Magnum/GL/Test/ContextTest.cpp b/src/Magnum/GL/Test/ContextTest.cpp
index af5c0132a..d8078e8d3 100644
--- a/src/Magnum/GL/Test/ContextTest.cpp
+++ b/src/Magnum/GL/Test/ContextTest.cpp
@@ -421,9 +421,8 @@ void ContextTest::extensions() {
             CORRADE_VERIFY(Int(e.coreVersion()) >= Int(e.requiredVersion()));
             bool coreVersionMismatch = e.coreVersion() != version
                 #if defined(MAGNUM_TARGET_GLES2) && defined(MAGNUM_TARGET_WEBGL)
-                /* These two are replaced by EXT_color_buffer_float for 2.0,
-                   but aren't core in WebGL 2 */
-                && e.index() != Extensions::EXT::color_buffer_half_float::Index
+                /* Replaced by EXT_color_buffer_float for 2.0 but not core in
+                   WebGL 2 */
                 && e.index() != Extensions::WEBGL::color_buffer_float::Index
                 #endif
                 ;
diff --git a/src/Magnum/GL/TextureFormat.h b/src/Magnum/GL/TextureFormat.h
index 3e34f77ca..9a870c0e3 100644
--- a/src/Magnum/GL/TextureFormat.h
+++ b/src/Magnum/GL/TextureFormat.h
@@ -739,9 +739,11 @@ enum class TextureFormat: GLenum {
      *      in WebGL 1.0.
      * @requires_webgl20 Extension @webgl_extension{OES,texture_half_float_linear}
      *      for filtering using @ref SamplerFilter::Linear in WebGL 1.0.
-     * @requires_webgl_extension Extension @webgl_extension{EXT,color_buffer_float}
-     *      to use as a render target in WebGL 2.0; use @ref TextureFormat::R16UI
-     *      or @ref TextureFormat::R16I instead if not available. Only three-
+     * @requires_webgl_extension Extension
+     *      @webgl_extension{EXT,color_buffer_half_float} or
+     *      @webgl_extension{EXT,color_buffer_float} to use as a render target
+     *      in WebGL 2.0; use @ref TextureFormat::R16UI or
+     *      @ref TextureFormat::R16I instead if not available. Only three-
      *      and four-component half-float texture formats can be used as
      *      a render target in WebGL 1.0, see @ref TextureFormat::RGBA16F for
      *      more information.
@@ -767,9 +769,11 @@ enum class TextureFormat: GLenum {
      *      in WebGL 1.0 instead.
      * @requires_webgl20 Extension @webgl_extension{OES,texture_half_float_linear}
      *      for filtering using @ref SamplerFilter::Linear in WebGL 1.0.
-     * @requires_webgl_extension Extension @webgl_extension{EXT,color_buffer_float}
-     *      to use as a render target in WebGL 2.0; use @ref TextureFormat::RG16UI
-     *      or @ref TextureFormat::RG16I instead if not available. Only three-
+     * @requires_webgl_extension Extension
+     *      @webgl_extension{EXT,color_buffer_half_float} or
+     *      @webgl_extension{EXT,color_buffer_float} to use as a render target
+     *      in WebGL 2.0; use @ref TextureFormat::RG16UI or
+     *      @ref TextureFormat::RG16I instead if not available. Only three-
      *      and four-component half-float texture formats can be used as
      *      a render target in WebGL 1.0, see @ref TextureFormat::RGBA16F for
      *      more information.
@@ -813,11 +817,14 @@ enum class TextureFormat: GLenum {
      * @requires_webgl20 Use @ref TextureFormat::RGBA in combination with
      *      @ref PixelType::Half (@webgl_extension{OES,texture_half_float}) in
      *      WebGL 1.0 instead.
-     * @requires_webgl_extension Extension @webgl_extension{EXT,color_buffer_float}
-     *      to use as a render target in WebGL 2.0. Use @ref TextureFormat::RGBA16UI
-     *      or @ref TextureFormat::RGBA16I instead if not available. Use
+     * @requires_webgl_extension Extension
+     *      @webgl_extension{EXT,color_buffer_half_float} or
+     *      @webgl_extension{EXT,color_buffer_float} to use as a render target
+     *      in WebGL 2.0. Use @ref TextureFormat::RGBA16UI or
+     *      @ref TextureFormat::RGBA16I instead if not available. Use
      *      @ref TextureFormat::RGBA in combination with @ref PixelType::Half
-     *      (@webgl_extension{EXT,color_buffer_half_float}) in WebGL 1.0 instead.
+     *      (@webgl_extension{EXT,color_buffer_half_float}) in WebGL 1.0
+     *      instead.
      */
     RGBA16F = GL_RGBA16F,
 
@@ -1014,6 +1021,9 @@ enum class TextureFormat: GLenum {
      *      OpenGL ES 2.0.
      * @requires_webgl20 Only normalized integral formats are available in
      *      WebGL 1.0.
+     * @requires_webgl_extension Extension
+     *      @webgl_extension{EXT,color_buffer_float} to use as a render target
+     *      in WebGL 2.0.
      */
     R11FG11FB10F = GL_R11F_G11F_B10F,