Some hints when saving transparent gifs.
First and foremost : If your graphic will not be animated and you know the approximate colour of your page use it as your background colour ( plain, of course, no pattern )
Remember that PSP will put in a colour anyway to be the transparent colour.
Saving with your own background colour is fairly simple so I'll cover that first.
The thing to remember is "The lower the tolerance the more added anti-alias colours will be kept and the smoother the result.
Raising the tolerance gradually takes away the effect until you have a more jagged edge
Saving with "Existing Transparency" is a little more complicated and is the only way possible in Animation Shop. (AS)
I will do PSP first because AS is not nearly so user friendly.
Click on the Partial Transparency tab and play around with the controls to get the best result.
Zoom in to make sure you know what you are getting.
The way you see here is about where I usually end up but different graphics have different requirements so experiment.
If you have trouble getting a good edge in AS go back and save the gif from PSP and make a note of the settings you use.
They can be duplicated in AS although the format is slightly different and there is no preview.
Once you have your graphic ready to save in AS
Go to File > Optimization Wizard - or - Shift Z.
Make it easy on yourself and create a new graphic in case you want to try again.
On the next page go to "Customize"
Then click on the "Partial Transparency" tab.
The only difference between PSP and AS here is that AS uses 256 colours instead of % in the opacity scale.
Luckily the percentage does show so that you can copy what you did in PSP.
Once you have that correct click "OK" and "Next" until the end.
Now your animation is ready to save.