Because colors 0x00..0xc0 are compressed better than colors 0xc1..0xff, good palette sorting is important. It's usually (but not always) enough to move the most-common colors into palette positions 0x00..0xc0, and least-used to palette positions 0xc1..0xff. Complete algorithm of sorting pallette is to count how many times a color appears 63N+1 (for nonnegative integer N) times it a row, as only in such cases it's possible to use unprefixed color values to improve compression, and move colors with higher count into indexes 0x00..0xc0, and all other to 0xc1..0xff. This is warranted to produce optimal results.
This compression algorithm is very fast and takes very little memory, but its not very efficient, especially in compressing real-world images.