diff --git a/src/Magnum/CubeMapTexture.cpp b/src/Magnum/CubeMapTexture.cpp
index 2e5e917c9..569a3dbd9 100644
--- a/src/Magnum/CubeMapTexture.cpp
+++ b/src/Magnum/CubeMapTexture.cpp
@@ -109,8 +109,7 @@ void CubeMapTexture::compressedImage(const Int level, CompressedImage3D& image)
     createIfNotAlready();
 
     const Vector3i size{imageSize(level), 6};
-    GLint textureDataSize;
-    (this->*Context::current()->state().texture->getCubeLevelParameterivImplementation)(level, GL_TEXTURE_COMPRESSED_IMAGE_SIZE, &textureDataSize);
+    const GLint textureDataSize = (this->*Context::current()->state().texture->getCubeLevelCompressedImageSizeImplementation)(level);
     const std::size_t dataSize = Implementation::compressedImageDataSizeFor(image, size, textureDataSize);
     GLint format;
     (this->*Context::current()->state().texture->getCubeLevelParameterivImplementation)(level, GL_TEXTURE_INTERNAL_FORMAT, &format);
@@ -135,8 +134,7 @@ void CubeMapTexture::compressedImage(const Int level, CompressedBufferImage3D& i
     createIfNotAlready();
 
     const Vector3i size{imageSize(level), 6};
-    GLint textureDataSize;
-    (this->*Context::current()->state().texture->getCubeLevelParameterivImplementation)(level, GL_TEXTURE_COMPRESSED_IMAGE_SIZE, &textureDataSize);
+    const GLint textureDataSize = (this->*Context::current()->state().texture->getCubeLevelCompressedImageSizeImplementation)(level);
     const std::size_t dataSize = Implementation::compressedImageDataSizeFor(image, size, textureDataSize);
     GLint format;
     (this->*Context::current()->state().texture->getCubeLevelParameterivImplementation)(level, GL_TEXTURE_INTERNAL_FORMAT, &format);
@@ -199,8 +197,9 @@ BufferImage2D CubeMapTexture::image(const Coordinate coordinate, const Int level
 
 void CubeMapTexture::compressedImage(const Coordinate coordinate, const Int level, CompressedImage2D& image) {
     const Vector2i size = imageSize(level);
-    GLint textureDataSize;
-    (this->*Context::current()->state().texture->getCubeLevelParameterivImplementation)(level, GL_TEXTURE_COMPRESSED_IMAGE_SIZE, &textureDataSize);
+    /* The function returns size of all six faces, divide the result to get size
+       of one face */
+    const GLint textureDataSize = (this->*Context::current()->state().texture->getCubeLevelCompressedImageSizeImplementation)(level)/6;
     const std::size_t dataSize = Implementation::compressedImageDataSizeFor(image, size, textureDataSize);
     GLint format;
     (this->*Context::current()->state().texture->getCubeLevelParameterivImplementation)(level, GL_TEXTURE_INTERNAL_FORMAT, &format);
@@ -223,8 +222,9 @@ CompressedImage2D CubeMapTexture::compressedImage(const Coordinate coordinate, c
 
 void CubeMapTexture::compressedImage(const Coordinate coordinate, const Int level, CompressedBufferImage2D& image, const BufferUsage usage) {
     const Vector2i size = imageSize(level);
-    GLint textureDataSize;
-    (this->*Context::current()->state().texture->getCubeLevelParameterivImplementation)(level, GL_TEXTURE_COMPRESSED_IMAGE_SIZE, &textureDataSize);
+    /* The function returns size of all six faces, divide the result to get size
+       of one face */
+    const GLint textureDataSize = (this->*Context::current()->state().texture->getCubeLevelCompressedImageSizeImplementation)(level)/6;
     const std::size_t dataSize = Implementation::compressedImageDataSizeFor(image, size, textureDataSize);
     GLint format;
     (this->*Context::current()->state().texture->getCubeLevelParameterivImplementation)(level, GL_TEXTURE_INTERNAL_FORMAT, &format);
@@ -362,6 +362,38 @@ void CubeMapTexture::getLevelParameterImplementationDSAEXT(const GLint level, co
 #endif
 #endif
 
+#if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
+GLint CubeMapTexture::getLevelCompressedImageSizeImplementationDefault(const GLint level) {
+    bindInternal();
+    /* Using only parameters of +X in pre-DSA code path and assuming that all
+       other faces are the same */
+    GLint value;
+    glGetTexLevelParameteriv(GL_TEXTURE_CUBE_MAP_POSITIVE_X, level, GL_TEXTURE_COMPRESSED_IMAGE_SIZE, &value);
+
+    /* Size of all six faces */
+    return value*6;
+}
+
+#ifndef MAGNUM_TARGET_GLES
+GLint CubeMapTexture::getLevelCompressedImageSizeImplementationDSA(const GLint level) {
+    GLint value;
+    glGetTextureLevelParameteriv(_id, level, GL_TEXTURE_COMPRESSED_IMAGE_SIZE, &value);
+    return value;
+}
+
+GLint CubeMapTexture::getLevelCompressedImageSizeImplementationDSAEXT(const GLint level) {
+    _flags |= ObjectFlag::Created;
+    /* Using only parameters of +X in pre-DSA code path and assuming that all
+       other faces are the same */
+    GLint value;
+    glGetTextureLevelParameterivEXT(_id, GL_TEXTURE_CUBE_MAP_POSITIVE_X, level, GL_TEXTURE_COMPRESSED_IMAGE_SIZE, &value);
+
+    /* Size of all six faces */
+    return value*6;
+}
+#endif
+#endif
+
 #ifndef MAGNUM_TARGET_GLES
 void CubeMapTexture::getImageImplementationDefault(const Coordinate coordinate, const GLint level, const Vector2i&, const PixelFormat format, const PixelType type, std::size_t, GLvoid* const data) {
     bindInternal();
diff --git a/src/Magnum/CubeMapTexture.h b/src/Magnum/CubeMapTexture.h
index 9f0a4ffc8..4e4b0c4d9 100644
--- a/src/Magnum/CubeMapTexture.h
+++ b/src/Magnum/CubeMapTexture.h
@@ -952,6 +952,14 @@ class MAGNUM_EXPORT CubeMapTexture: public AbstractTexture {
         #endif
         #endif
 
+        #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
+        GLint MAGNUM_LOCAL getLevelCompressedImageSizeImplementationDefault(GLint level);
+        #ifndef MAGNUM_TARGET_GLES
+        GLint MAGNUM_LOCAL getLevelCompressedImageSizeImplementationDSA(GLint level);
+        GLint MAGNUM_LOCAL getLevelCompressedImageSizeImplementationDSAEXT(GLint level);
+        #endif
+        #endif
+
         #ifndef MAGNUM_TARGET_GLES
         void MAGNUM_LOCAL getImageImplementationDefault(Coordinate coordinate, GLint level, const Vector2i& size, PixelFormat format, PixelType type, std::size_t dataSize, GLvoid* data);
         void MAGNUM_LOCAL getImageImplementationDSA(Coordinate coordinate, GLint level, const Vector2i& size, PixelFormat format, PixelType type, std::size_t dataSize, GLvoid* data);
diff --git a/src/Magnum/Implementation/TextureState.cpp b/src/Magnum/Implementation/TextureState.cpp
index 0ece7be34..ec127405e 100644
--- a/src/Magnum/Implementation/TextureState.cpp
+++ b/src/Magnum/Implementation/TextureState.cpp
@@ -136,6 +136,7 @@ TextureState::TextureState(Context& context, std::vector<std::string>& extension
         setBufferRangeImplementation = &BufferTexture::setBufferRangeImplementationDSA;
 
         getCubeLevelParameterivImplementation = &CubeMapTexture::getLevelParameterImplementationDSA;
+        getCubeLevelCompressedImageSizeImplementation = &CubeMapTexture::getLevelCompressedImageSizeImplementationDSA;
         cubeSubImageImplementation = &CubeMapTexture::subImageImplementationDSA;
         cubeCompressedSubImageImplementation = &CubeMapTexture::compressedSubImageImplementationDSA;
 
@@ -161,6 +162,7 @@ TextureState::TextureState(Context& context, std::vector<std::string>& extension
         setBufferRangeImplementation = &BufferTexture::setBufferRangeImplementationDSAEXT;
 
         getCubeLevelParameterivImplementation = &CubeMapTexture::getLevelParameterImplementationDSAEXT;
+        getCubeLevelCompressedImageSizeImplementation = &CubeMapTexture::getLevelCompressedImageSizeImplementationDSAEXT;
         cubeSubImageImplementation = &CubeMapTexture::subImageImplementationDSAEXT;
         cubeCompressedSubImageImplementation = &CubeMapTexture::compressedSubImageImplementationDSAEXT;
 
@@ -199,6 +201,7 @@ TextureState::TextureState(Context& context, std::vector<std::string>& extension
 
         #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
         getCubeLevelParameterivImplementation = &CubeMapTexture::getLevelParameterImplementationDefault;
+        getCubeLevelCompressedImageSizeImplementation = &CubeMapTexture::getLevelCompressedImageSizeImplementationDefault;
         #endif
         cubeSubImageImplementation = &CubeMapTexture::subImageImplementationDefault;
         cubeCompressedSubImageImplementation = &CubeMapTexture::compressedSubImageImplementationDefault;
diff --git a/src/Magnum/Implementation/TextureState.h b/src/Magnum/Implementation/TextureState.h
index 81ab20a42..85ceb0b7b 100644
--- a/src/Magnum/Implementation/TextureState.h
+++ b/src/Magnum/Implementation/TextureState.h
@@ -99,6 +99,7 @@ struct TextureState {
 
     #if !defined(MAGNUM_TARGET_GLES2) && !defined(MAGNUM_TARGET_WEBGL)
     void(CubeMapTexture::*getCubeLevelParameterivImplementation)(GLint, GLenum, GLint*);
+    GLint(CubeMapTexture::*getCubeLevelCompressedImageSizeImplementation)(GLint);
     #endif
     #ifndef MAGNUM_TARGET_GLES
     void(CubeMapTexture::*getCubeImageImplementation)(CubeMapTexture::Coordinate, GLint, const Vector2i&, PixelFormat, PixelType, std::size_t, GLvoid*);