A technique is described for compressing textures for use in a graphics application, such as a 3D game application. The technique includes parsing first-compressed texture information (e.g., S3TC texture information) into respective components of the first-compressed texture information (such as main color information, color index information, main alpha information, and alpha index information). The technique then further compresses the respective components to yield second-compressed texture information (referred to as modified compressed texture information or MCT texture information). The MCT texture information can be stored and then decoded to reconstruct the original S3TC texture information for use in the graphics application. Compared to the use of unmodified S3TC texture information, the technique allows more economical storage of texture information, as well as more efficient loading of the texture information from storage to memory.