1. Open up your GIF file in Imageready. Go to Window > Optimize. You will see a window like this:

2. Click on the Optimize tab on your GIF window. This is how your file will look when saved as a GIF. At the bottom is the approximate file size.

3. Let's take a look at the Optimize window we opened earlier. When you click Preset, you will see a number of options from the drop-down menu. Remember you can only save an animation as a GIF if you want it to move. 128 Dithered means it will have 128 colors and small, grainy dots over the GIF. Observe the Color Table section. Generally I prefer the "Selective" option in the Reduction drop-down menu, but feel free to play around with the other settings. Below is the number of colors you want your GIF to have. The more colors there are, the better your GIF will look but the file size will also be higher (as you play around with the settings, remember to check the status bar in step 2 that shows how large your file size will be). Look down at the Dither sectoin. For the Method, you'd usually stick with Diffusion, but you can also turn off the Dither. You can change the amount of dithering below, too. The higher the percentage, the more grainy dots in your GIF and the larger your file size will be. I'm not a big fan of dithering so I prefer to turn it off so the GIF doesn't look so grainy.

4. That about sums up the basics of lowering GIF file size. You will basically have to find the right balance between the image quality of the optimized GIF and its file size. And remember to save by going to File > Save Optimized As! Here are a few other simple methods to lowering GIF size: