Gifpress

Gifpress is a special-purpose file compression utility for DOS. It compresses only GIF image files, to its native .GPS format. It was developed by John Callicotte, and distributed as shareware.

A GPS file can be decompressed back to a GIF file that is functionally identical to the original, but not necessarily byte-for-byte identical.

Format details
There's clear evidence that Gifpress uses the Cx data compression toolkit (v2.01) by Eugene Nelson and Four Lakes Computing.

Identification
It's not known how to identify a GPS file from its contents, though in limited testing, the bytes always appeared at offset 2.