You can reduce the size of your GIF-compressed image by encouraging horizontally continuous areas of solid color. Dithering, though it produces a pleasing approximation of color depth, introduces noise that can not be compressed well. To keep your GIF files small, remove noise by filling solid areas with a "fill" brush, and do not use dithering to optimize the palette.
Dithered image: 29658 bytes
Non-dithered image: 23130 bytes
Dithering interrupts areas of solid color with noisy pointillism. Since GIF compression is more effective with horizontally continugous solid color, dithering increases file size.
Dithered
Not dithered