Multi-mode decoding and encoding of texture blocks are disclosed wherein in a default decoding and encoding mode all bits of a codeword sequence are available as payload bits for representing texel values of the texels in the texture block. In an auxiliary encoding and decoding mode one less bit of the codeword sequence is available as payload bits. The auxiliary mode is employed as a complement to the default mode and will be used to process those texture blocks, which the default mode handles poorly.