Method of reversible compression of low-order bits in digital images that uses image palette as a look up table for high versus low order bit fragments and replaces actual low-order bit fragments in the image by relative sequential indexes that identify the position of correspondent low-order bit fragment in palette array. Said relative sequential indexes are smaller than low-order bit fragments because they are introduced and incremented within the same high-order bit expression in palette array and have significantly different statistical distribution properties compared to distribution of original low-order bit fragments. For successful reconstruction of said low-order bit fragments from said relative sequential indexes the critical part of palette array is saved in compressed data. In spite of additional data buffer the method significantly improves compression ratio and has dual effect: first is compression of low-order bits and second is possibility to ignore then low-order bits in data modeling.