Techniques relating to serial processing of pixels in a texture processing pipeline. In some embodiments, the pipeline receives pixel data for a set of pixels in parallel but processes the pixels in the set serially in a pipelined fashion. In some embodiments, the pipeline includes a stage configured to retain texel data for use by a subsequently processed pixel. They may allow overlapping texels to be fetched once for the set of pixels rather than multiple times for different pixels in the set. In some embodiments, the pipeline uses a selected ordering of serial processing for the pixels, where the ordering increases the potential for texel overlap, relative to one or more other orderings.