Animated GIF optimization

I was constructing an animated GIF to use as my avatar (100X100, 7 frames of animation), and I was unable to get the memory could less than 24KB. Does anyone know of any programs/techniques to improve this?

I use Jasc’s Animation Shop 3, which has a slider allowing you to strike a balance between quality and size. Want to send me the gif and I’ll see what I can do?