There's JPEG 2000, which is nothing like classic JPEG. It doesn't have the artifacts classic JPEG introduces at sharp edges, so you can read text. It has more color depth if you want it. It also doesn't mess up non-color data such as normal maps the way classic JPEG does.

JPEG 2000 is not used much. Decoding is slow, and encoding is slower. The decoders are either buggy or proprietary. It has way too many options internally. The big users of JPEG 2000 are medical. It has a "lossless" mode, and medical imagery is usually stored lossless because you really don't want compression artifacts in X-rays.

(I've been struggling with JPEG 2000 recently. Second Life and Open Simulator use it for asset storage. Some images won't decompress properly with OpenJPEG, a free decoder. I finally found out why. There's a field used for "personal health information" in JPEG 2000. This is where the patient name and such go in a CAT scan. That feature was added after the original version. Some older images apparently have junk in that field, which causes problems.)