File compression and Winzip
Time to back up a little.
File compression was not originally developed for graphic files. The most popular and common file compression in current use is the ZIP format. And the most popular program is Winzip. Other popular compression formats include ARJ, LZH, Gzip, TAR, And CAB.
Winzip allow you to compress any type of computer file, text, programs, graphics, etc. If you wish to store or save large BMP Images, one reasonable method would be to compress them using the ZIP Format.

A Basic BMP File
192 K
Bitmap Zipped
76 K
This can archive a reasonable compression and sometime that is the best that you can get. If you want and need full 24 Bit color images saved perfectly bit for bit, this may be your only option
Next, we'll compress the same file in the GIF format and see what happens.

The same file saved as a GIF
28 K
Bitmap Zipped
28 K
No Difference!

LZW Compression
The reason is that the GIF Format uses the same "index" method of compression that the ZIP format does. Both methods use an index of commonly repeated data to conserve space. The important people behind this were Jacob Ziv, Abraham Lempel and Terry Welch : Lempel-Ziv-Welch, hence LZW.
Take for example this passage from "A Tale of Two Cities".
     It was the best of times,
     it was the worst of times,
     it was the age of wisdom,
     it was the age of foolishness.

With an index method of compression you would get the following

     Begin File
     *1 = "it was the" , *2=times, *3="age of"
     *1 best of *2,
     *1 worst of *2,
     *1 *3 wisdom,
     *1 *3 foolishness,
     End File
The real version uses a more complication algorithm to determine the best possible replacements but you get the general idea.
I would highly recommend this article by "How things work".
How Stuff Works

Further Information

Next -----> 8. File compression and Data Loss