diff --git a/src/AbstractTexture.h b/src/AbstractTexture.h
index 76657184f..0ad26b57d 100644
--- a/src/AbstractTexture.h
+++ b/src/AbstractTexture.h
@@ -472,25 +472,11 @@ class MAGNUM_EXPORT AbstractTexture {
              * @param target            %Target
              * @param mipLevel          Mip level
              * @param internalFormat    Internal texture format
-             * @param dimensions        %Texture dimensions
-             * @param colorFormat       Color format of passed data
-             * @param type              Data type
-             * @param data              %Texture data
-             *
-             * Calls `glTexImage1D`, `glTexImage2D`, `glTexImage3D` depending
-             * on dimension count.
-             */
-            inline static void set(Target target, GLint mipLevel, InternalFormat internalFormat, const Math::Vector<GLsizei, textureDimensions>& dimensions, ColorFormat colorFormat, Type type, const void* data);
-
-            /**
-             * @brief Set texture data from image
-             * @param target            %Target
-             * @param mipLevel          Mip level
-             * @param internalFormat    Internal texture format
              * @param image             Image, BufferedImage or for example
              *      Trade::ImageData of the same dimension count
              *
-             * Calls set() with image data.
+             * Calls `glTexImage1D`, `glTexImage2D`, `glTexImage3D` depending
+             * on dimension count.
              */
             template<class T> inline static void set(Target target, GLint mipLevel, InternalFormat internalFormat, T* image);
 
@@ -499,25 +485,11 @@ class MAGNUM_EXPORT AbstractTexture {
              * @param target            %Target
              * @param mipLevel          Mip level
              * @param offset            Offset where to put data in the texture
-             * @param dimensions        %Texture dimensions
-             * @param colorFormat       Color format of passed data
-             * @param type              Data type
-             * @param data              %Texture data
-             *
-             * Calls `glTexSubImage1D`, `glTexSubImage2D`, `glTexSubImage3D`
-             * depending on dimension count.
-             */
-            inline static void setSub(SubTarget target, GLint mipLevel, const Math::Vector<GLint, textureDimensions>& offset, const Math::Vector<GLsizei, textureDimensions>& dimensions, ColorFormat colorFormat, Type type, const void* data);
-
-            /**
-             * @brief Set texture subdata from image
-             * @param target            %Target
-             * @param mipLevel          Mip level
-             * @param offset            Offset where to put data in the texture
              * @param image             Image, BufferedImage or for example
              *      Trade::ImageData of the same dimension count
              *
-             * Calls setSub() with image data.
+             * Calls `glTexSubImage1D`, `glTexSubImage2D`, `glTexSubImage3D`
+             * depending on dimension count.
              */
             template<class T> inline static void setSub(Target target, GLint mipLevel, const Math::Vector<GLint, textureDimensions>& offset, T* image);
             #endif
@@ -581,20 +553,12 @@ template<> struct AbstractTexture::DataHelper<1> {
         glTexParameteri(static_cast<GLenum>(target), GL_TEXTURE_WRAP_S, static_cast<GLint>(wrapping.at(0)));
     }
 
-    inline static void set(Target target, GLint mipLevel, InternalFormat internalFormat, const Math::Vector<GLsizei, 1>& dimensions, ColorFormat colorFormat, Type type, const void* data) {
-        glTexImage1D(static_cast<GLenum>(target), mipLevel, internalFormat, dimensions.at(0), 0, static_cast<GLenum>(colorFormat), static_cast<GLenum>(type), data);
-    }
-
     template<class T> inline static void set(Target target, GLint mipLevel, InternalFormat internalFormat, T* image) {
-        set(target, mipLevel, internalFormat, image->dimensions(), image->colorFormat(), image->type(), image->data());
-    }
-
-    inline static void setSub(Target target, GLint mipLevel, const Math::Vector<GLint, 1>& offset, const Math::Vector<GLsizei, 1>& dimensions, ColorFormat colorFormat, Type type, const void* data) {
-        glTexSubImage1D(static_cast<GLenum>(target), mipLevel, offset.at(0), dimensions.at(0), static_cast<GLenum>(colorFormat), static_cast<GLenum>(type), data);
+        glTexImage1D(static_cast<GLenum>(target), mipLevel, internalFormat, image->dimensions().at(0), 0, static_cast<GLenum>(image->colorFormat()), static_cast<GLenum>(image->type()), image->data());
     }
 
     template<class T> inline static void setSub(Target target, GLint mipLevel, const Math::Vector<GLint, 1>& offset, T* image) {
-        setSub(target, mipLevel, offset, image->dimensions(), image->colorFormat(), image->type(), image->data());
+        glTexSubImage1D(static_cast<GLenum>(target), mipLevel, offset.at(0), image->dimensions().at(0), static_cast<GLenum>(image->colorFormat()), static_cast<GLenum>(image->type()), image->data());
     }
 };
 template<> struct AbstractTexture::DataHelper<2> {
@@ -618,20 +582,12 @@ template<> struct AbstractTexture::DataHelper<2> {
         glTexParameteri(static_cast<GLenum>(target), GL_TEXTURE_WRAP_T, static_cast<GLint>(wrapping.at(1)));
     }
 
-    inline static void set(Target target, GLint mipLevel, InternalFormat internalFormat, const Math::Vector<GLsizei, 2>& dimensions, ColorFormat colorFormat, Type type, const void* data) {
-        glTexImage2D(static_cast<GLenum>(target), mipLevel, internalFormat, dimensions.at(0), dimensions.at(1), 0, static_cast<GLenum>(colorFormat), static_cast<GLenum>(type), data);
-    }
-
     template<class T> inline static void set(Target target, GLint mipLevel, InternalFormat internalFormat, T* image) {
-        set(target, mipLevel, internalFormat, image->dimensions(), image->colorFormat(), image->type(), image->data());
-    }
-
-    inline static void setSub(Target target, GLint mipLevel, const Math::Vector<GLint, 2>& offset, const Math::Vector<GLsizei, 2>& dimensions, ColorFormat colorFormat, Type type, const void* data) {
-        glTexSubImage2D(static_cast<GLenum>(target), mipLevel, offset.at(0), offset.at(1), dimensions.at(0), dimensions.at(1), static_cast<GLenum>(colorFormat), static_cast<GLenum>(type), data);
+        glTexImage2D(static_cast<GLenum>(target), mipLevel, internalFormat, image->dimensions().at(0), image->dimensions().at(1), 0, static_cast<GLenum>(image->colorFormat()), static_cast<GLenum>(image->type()), image->data());
     }
 
     template<class T> inline static void setSub(Target target, GLint mipLevel, const Math::Vector<GLint, 2>& offset, T* image) {
-        setSub(target, mipLevel, offset, image->dimensions(), image->colorFormat(), image->type(), image->data());
+        glTexSubImage2D(static_cast<GLenum>(target), mipLevel, offset.at(0), offset.at(1), image->dimensions().at(0), image->dimensions().at(1), static_cast<GLenum>(image->colorFormat()), static_cast<GLenum>(image->type()), image->data());
     }
 };
 template<> struct AbstractTexture::DataHelper<3> {
@@ -648,20 +604,12 @@ template<> struct AbstractTexture::DataHelper<3> {
         glTexParameteri(static_cast<GLenum>(target), GL_TEXTURE_WRAP_R, static_cast<GLint>(wrapping.at(2)));
     }
 
-    inline static void set(Target target, GLint mipLevel, InternalFormat internalFormat, const Math::Vector<GLsizei, 3>& dimensions, ColorFormat colorFormat, Type type, const void* data) {
-        glTexImage3D(static_cast<GLenum>(target), mipLevel, internalFormat, dimensions.at(0), dimensions.at(1), dimensions.at(2), 0, static_cast<GLenum>(colorFormat), static_cast<GLenum>(type), data);
-    }
-
     template<class T> inline static void set(Target target, GLint mipLevel, InternalFormat internalFormat, T* image) {
-        set(target, mipLevel, internalFormat, image->dimensions(), image->colorFormat(), image->type(), image->data());
-    }
-
-    inline static void setSub(Target target, GLint mipLevel, const Math::Vector<GLint, 3>& offset, const Math::Vector<GLsizei, 3>& dimensions, ColorFormat colorFormat, Type type, const void* data) {
-        glTexSubImage3D(static_cast<GLenum>(target), mipLevel, offset.at(0), offset.at(1), offset.at(2), dimensions.at(0), dimensions.at(1), dimensions.at(2), static_cast<GLenum>(colorFormat), static_cast<GLenum>(type), data);
+        glTexImage3D(static_cast<GLenum>(target), mipLevel, internalFormat, image->dimensions().at(0), image->dimensions().at(1), image->dimensions().at(2), 0, static_cast<GLenum>(image->colorFormat()), static_cast<GLenum>(image->type()), image->data());
     }
 
     template<class T> inline static void setSub(Target target, GLint mipLevel, const Math::Vector<GLint, 3>& offset, T* image) {
-        setSub(target, mipLevel, offset, image->dimensions(), image->colorFormat(), image->type(), image->data());
+        glTexSubImage3D(static_cast<GLenum>(target), mipLevel, offset.at(0), offset.at(1), offset.at(2), image->dimensions().at(0), image->dimensions().at(1), image->dimensions().at(2), static_cast<GLenum>(image->colorFormat()), static_cast<GLenum>(image->type()), image->data());
     }
 };
 #endif
diff --git a/src/CubeMapTexture.h b/src/CubeMapTexture.h
index ce5d61c2b..b5d4a47aa 100644
--- a/src/CubeMapTexture.h
+++ b/src/CubeMapTexture.h
@@ -64,20 +64,9 @@ class CubeMapTexture: public Texture2D {
          */
         inline CubeMapTexture(GLint layer = 0): Texture(layer, Target::CubeMap) {}
 
-        template<class T> inline void setData(GLint mipLevel, InternalFormat internalFormat, const Math::Vector<GLsizei, Dimensions>& dimensions, ColorFormat colorFormat, const T* data) = delete;
         template<class T> void setData(GLint mipLevel, InternalFormat internalFormat, T* image) = delete;
-        template<class T> inline void setSubData(GLint mipLevel, const Math::Vector<GLint, Dimensions>& offset, const Math::Vector<GLsizei, Dimensions>& dimensions, ColorFormat colorFormat, const T* data) = delete;
         template<class T> void setSubData(GLint mipLevel, const Math::Vector<GLint, Dimensions>& offset, T* image) = delete;
 
-        /**
-         * @copydoc Texture::setData(GLint, InternalFormat, const Math::Vector<GLsizei, Dimensions>&, ColorFormat, const T*)
-         * @param coordinate   Coordinate
-         */
-        template<class T> inline void setData(Coordinate coordinate, GLint mipLevel, InternalFormat internalFormat, const Math::Vector<GLsizei, Dimensions>& dimensions, ColorFormat colorFormat, const T* data) {
-            bind();
-            DataHelper<Dimensions>::set(static_cast<Target>(coordinate), mipLevel, internalFormat, dimensions, colorFormat, TypeTraits<typename TypeTraits<T>::TextureType>::glType(), data);
-        }
-
         /**
          * @copydetails Texture::setData(GLint, InternalFormat, T*)
          * @param coordinate   Coordinate
@@ -87,15 +76,6 @@ class CubeMapTexture: public Texture2D {
             DataHelper<Dimensions>::set(static_cast<Target>(coordinate), mipLevel, internalFormat, image);
         }
 
-        /**
-         * @copydoc Texture::setSubData(GLint, const Math::Vector<GLint, Dimensions>&, const Math::Vector<GLsizei, Dimensions>&, ColorFormat, const T*)
-         * @param coordinate   Coordinate
-         */
-        template<class T> inline void setSubData(Coordinate coordinate, GLint mipLevel, const Math::Vector<GLint, Dimensions>& offset, const Math::Vector<GLsizei, Dimensions>& dimensions, ColorFormat colorFormat, const T* data) {
-            bind();
-            DataHelper<Dimensions>::setSub(static_cast<Target>(coordinate), mipLevel, offset, dimensions, colorFormat, TypeTraits<typename TypeTraits<T>::TextureType>::glType(), data);
-        }
-
         /**
          * @copydoc Texture::setSubData(GLint, const Math::Vector<GLint, Dimensions>&, T*)
          * @param coordinate   Coordinate
diff --git a/src/Texture.h b/src/Texture.h
index 3ed51d670..40cd11073 100644
--- a/src/Texture.h
+++ b/src/Texture.h
@@ -82,22 +82,6 @@ template<size_t textureDimensions> class Texture: public AbstractTexture {
          * @brief Set texture data
          * @param mipLevel          Mip level
          * @param internalFormat    Internal texture format
-         * @param dimensions        %Texture dimensions
-         * @param colorFormat       Color format of passed data. Data size per
-         *      color channel is detected from format of passed data array.
-         * @param data              %Texture data
-         *
-         * Sets texture from given data. The data are not deleted afterwards.
-         */
-        template<class T> inline void setData(GLint mipLevel, InternalFormat internalFormat, const Math::Vector<GLsizei, Dimensions>& dimensions, ColorFormat colorFormat, const T* data) {
-            bind();
-            DataHelper<Dimensions>::set(_target, mipLevel, internalFormat, dimensions, colorFormat, TypeTraits<typename TypeTraits<T>::TextureType>::glType(), data);
-        }
-
-        /**
-         * @brief Set texture data from image
-         * @param mipLevel          Mip level
-         * @param internalFormat    Internal texture format
          * @param image             Image, BufferedImage or for example
          *      Trade::ImageData of the same dimension count
          *
@@ -113,23 +97,6 @@ template<size_t textureDimensions> class Texture: public AbstractTexture {
          * @brief Set texture subdata
          * @param mipLevel          Mip level
          * @param offset            Offset where to put data in the texture
-         * @param dimensions        %Texture dimensions
-         * @param colorFormat       Color format of passed data. Data size per
-         *      color channel is detected from format of passed data array.
-         * @param data              %Texture data
-         *
-         * Sets texture subdata from given data. The data are not deleted
-         * afterwards.
-         */
-        template<class T> inline void setSubData(GLint mipLevel, const Math::Vector<GLint, Dimensions>& offset, const Math::Vector<GLsizei, Dimensions>& dimensions, ColorFormat colorFormat, const T* data) {
-            bind();
-            DataHelper<Dimensions>::setSub(_target, mipLevel, offset, dimensions, colorFormat, TypeTraits<typename TypeTraits<T>::TextureType>::glType(), data);
-        }
-
-        /**
-         * @brief Set texture subdata from image
-         * @param mipLevel          Mip level
-         * @param offset            Offset where to put data in the texture
          * @param image             Image, BufferedImage or for example
          *      Trade::ImageData of the same dimension count
          *