I tried Bright in 2005 but turned brown oil into purple (Jutocsa advised same thing), maybe newer version is better.
This is how I save a 256 color image in Photoshop v12, first as png then resave it as bmp.
Theres no other software I know about where you could select the color reduction algorithm (blue drop down list in the pic) which is important to have best quality.
Best result = biggest size (size is in lower left corner).
results:
left side / 8 bit
right side / 24 bit
100%
200%
And this is what happens to the color table when somebody not familiar with Photoshop starts to add his colorful skinner logos:
