The result of attempting to save "Anti-alias" graphics as transparent gifs

In PSP there are quite a few things you can try when saving a gif with anti-aliased edges for use on any background but by far the best way is to avoid it completely.
At least your vertical and horizontal lines will be smooth and curves will be as close as possible to correct.
To achieve this I always turn off "Anti-alias" when adding text or drawing any outside edges for this kind of graphic.

Since every PSPer's nemeses is the transparent background snow globe I will use it as an example.

If you intend to make snowglobes you should first decide on a suitable size and make a base graphic which includes the actual globe as the top layer.
How to make a snowglobe.
This will allow you to make the outside of the globe with anti-alias turned off and if you do not resize the graphic the edges will be ok. ( Maybe not perfect but as good as possible )
In the following graphic the left one has anti-alias turned off.
As you can see it looks exactly the same on any background whereas the other one does not.

Next "Some hints"