diff --git a/src/Magnum/DebugTools/Test/TextureImageGLTest.cpp b/src/Magnum/DebugTools/Test/TextureImageGLTest.cpp
index ac87bfc69..b1af30676 100644
--- a/src/Magnum/DebugTools/Test/TextureImageGLTest.cpp
+++ b/src/Magnum/DebugTools/Test/TextureImageGLTest.cpp
@@ -38,6 +38,7 @@
 #include "Magnum/GL/PixelFormat.h"
 #include "Magnum/GL/Texture.h"
 #include "Magnum/GL/TextureFormat.h"
+#include "Magnum/Math/Half.h"
 #include "Magnum/Math/Range.h"
 
 #ifndef MAGNUM_TARGET_GLES2
@@ -73,6 +74,8 @@ struct TextureImageGLTest: GL::OpenGLTester {
     void subImage2DUInt();
     void subImage2DFloat();
     void subImage2DFloatGeneric();
+    void subImage2DHalf();
+    void subImage2DHalfGeneric();
     #endif
 };
 
@@ -96,10 +99,14 @@ TextureImageGLTest::TextureImageGLTest() {
               &TextureImageGLTest::subImage2DUInt,
               &TextureImageGLTest::subImage2DFloat,
               &TextureImageGLTest::subImage2DFloatGeneric,
+              &TextureImageGLTest::subImage2DHalf,
+              &TextureImageGLTest::subImage2DHalfGeneric,
               #endif
               });
 }
 
+using namespace Math::Literals;
+
 constexpr UnsignedByte Data2D[] = { 0x00, 0x01, 0x02, 0x03,
                                     0x04, 0x05, 0x06, 0x07,
                                     0x08, 0x09, 0x0a, 0x0b,
@@ -422,6 +429,46 @@ void TextureImageGLTest::subImage2DFloatGeneric() {
         Containers::arrayView(Data2DFloat),
         TestSuite::Compare::Container);
 }
+
+const Half Data2DHalf[] = { 1.0_h,
+                            3.14159_h,
+                            2.71828_h,
+                            1.41421_h };
+
+void TextureImageGLTest::subImage2DHalf() {
+    GL::Texture2D texture;
+    texture
+        .setStorage(1, GL::TextureFormat::R16F, Vector2i{2})
+        .setSubImage(0, {}, ImageView2D{GL::PixelFormat::Red, GL::PixelType::Half, Vector2i{2}, Data2DHalf});
+
+    Image2D image = textureSubImage(texture, 0, {{}, Vector2i{2}}, {GL::PixelFormat::Red, GL::PixelType::Half});
+    MAGNUM_VERIFY_NO_GL_ERROR();
+    CORRADE_COMPARE(image.size(), Vector2i{2});
+    CORRADE_COMPARE(image.format(), pixelFormatWrap(GL::PixelFormat::Red));
+    CORRADE_COMPARE(GL::PixelType(image.formatExtra()), GL::PixelType::Half);
+    CORRADE_COMPARE(image.pixelSize(), 2);
+    CORRADE_COMPARE_AS(Containers::arrayCast<Half>(image.data()),
+        Containers::arrayView(Data2DHalf),
+        TestSuite::Compare::Container);
+}
+
+void TextureImageGLTest::subImage2DHalfGeneric() {
+    GL::Texture2D texture;
+    texture
+        .setStorage(1, GL::TextureFormat::R16F, Vector2i{2})
+        .setSubImage(0, {}, ImageView2D{GL::PixelFormat::Red, GL::PixelType::Half, Vector2i{2}, Data2DHalf});
+
+    Image2D image = textureSubImage(texture, 0, {{}, Vector2i{2}}, {PixelFormat::R16F});
+    MAGNUM_VERIFY_NO_GL_ERROR();
+    CORRADE_COMPARE(image.size(), Vector2i{2});
+    CORRADE_COMPARE(image.format(), PixelFormat::R16F);
+    CORRADE_COMPARE(image.formatExtra(), 0);
+    CORRADE_COMPARE(image.pixelSize(), 2);
+    CORRADE_COMPARE_AS(Containers::arrayCast<Half>(image.data()),
+        Containers::arrayView(Data2DHalf),
+        TestSuite::Compare::Container);
+}
+
 #endif
 
 }}}}
diff --git a/src/Magnum/DebugTools/TextureImage.cpp b/src/Magnum/DebugTools/TextureImage.cpp
index f874bcf04..56b65a4fb 100644
--- a/src/Magnum/DebugTools/TextureImage.cpp
+++ b/src/Magnum/DebugTools/TextureImage.cpp
@@ -115,9 +115,27 @@ void textureSubImage(GL::Texture2D& texture, const Int level, const Range2Di& ra
     }
     #endif
 
+    /* While I cannot reproduce this on any drivers I tried, not even on WebGL,
+       the ES3.0 and 3.1 spec says that Float isn't guaranteed to be supported,
+       only UnsignedByte and Int or UnsignedInt. I could probably do some
+       comparison against fb.implementationColorReadFormat() but this is more
+       straightforward.
+
+       ES3.2 says Float is supported. What still isn't guaranteed to be
+       supported are one-, two- and three-component formats, but so far I
+       didn't have a problem with these anywhere.
+
+       Half floats aren't guaranteed to be supported either, but given that I
+       cannot reproduce this issue anywhere anymore, I don't think I should
+       waste time implementing a half-float variant. */
+    /** @todo or just remove this altogether? */
     #if defined(MAGNUM_TARGET_GLES) && !defined(MAGNUM_TARGET_GLES2)
     GL::PixelType type = GL::pixelType(image.format(), image.formatExtra());
-    if(type == GL::PixelType::Float) {
+    if(type == GL::PixelType::Float
+        #ifndef MAGNUM_TARGET_WEBGL
+        && !GL::Context::current().isVersionSupported(GL::Version::GLES320)
+        #endif
+    ) {
         GL::TextureFormat textureFormat;
         GL::PixelFormat reinterpretFormat;
         GL::PixelFormat format = GL::pixelFormat(image.format());
@@ -224,6 +242,11 @@ void textureSubImage(GL::CubeMapTexture& texture, const GL::CubeMapCoordinate co
     GL::Framebuffer fb{range};
     fb.attachCubeMapTexture(GL::Framebuffer::ColorAttachment{0}, texture, coordinate, level);
 
+    /* Compared to textureSubImage(GL::Texture2D&), here's no specialized code
+       path for float formats, as it's impossible to sample it in a shader with
+       2D coordinates. It's also questionable if that's still needed. */
+    /** @todo or just remove this altogether? */
+
     CORRADE_ASSERT(fb.checkStatus(GL::FramebufferTarget::Read) == GL::Framebuffer::Status::Complete,
         "DebugTools::textureSubImage(): texture format not framebuffer-readable:" << fb.checkStatus(GL::FramebufferTarget::Read), );
 
diff --git a/src/Magnum/DebugTools/TextureImage.h b/src/Magnum/DebugTools/TextureImage.h
index 7d75a3608..5b82a8a97 100644
--- a/src/Magnum/DebugTools/TextureImage.h
+++ b/src/Magnum/DebugTools/TextureImage.h
@@ -50,11 +50,13 @@ is available, it's just an alias to @ref GL::Texture2D::subImage().
 The function expects that @p texture has a @ref GL::TextureFormat that's
 framebuffer-readable and that the @ref GL::PixelFormat and @ref GL::PixelType
 combination or the generic @relativeref{Magnum,PixelFormat} is compatible with
-it. In addition, on OpenGL ES 3.0, images with @ref GL::PixelType::Float
-are supported --- they are reinterpreted as @ref GL::PixelType::UnsignedInt
-using an additional shader and the @glsl floatBitsToUint() @ce GLSL function
-and then reinterpreted back to @ref GL::PixelType::Float when read to client
-memory.
+it. On OpenGL ES 3.0 and 3.1, @ref GL::PixelType::Float isn't guaranteed to be
+supported for reading so such images are reinterpreted as
+@ref GL::PixelType::UnsignedInt using an additional shader and the
+@glsl floatBitsToUint() @ce GLSL function and then reinterpreted back to
+@ref GL::PixelType::Float when read to client memory. On OpenGL ES 3.2 and on
+desktop GL, @ref GL::PixelType::Float is guaranteed to be supported. No similar
+treatment is done for any other types.
 
 @note This function is available only if Magnum is compiled with
     @ref MAGNUM_TARGET_GL "TARGET_GL" enabled (done by default). See