This is perhaps the most important part of the compression process, as it's where you'll decide which 256 colors will be used in your image. We can illustrate this with an example, in which the gradient button below is the original image. The following comparison shows the same image saved with each of the nine options. That aside, it seems fairly clear that Adaptive and Optimized are the best options.
Old habits die hard, and there are designers that still insist on using Web safe palettes.
Smoothing As is the case with JPG compression, smoothing should only be used in small amounts and only when absolutely needed to remove GIF artifacts such as color banding or a grainy appearance. As is also the case with JPG, smoothing will usually decrease file size, but will also decrease the sharpness of your image. To This is a relatively new option in GIF compression and one that you will occasionally find to be extremely useful. The option is only available with the Optimized Palette. For example, if your image contains a model's face on a blurred skyscape background, the model's face will obviously be the focal point of the image.