Thank you very much for all the info.

I tried Pencil, and I think it might be just what I'm looking for. Even though the latest version is still in the beta stage, it allows gif and png sequences to be imported and exported and allows layered animations as well. Unless I come across a better program, I think I'll stick with Pencil for the time being (I mean, it's free -- how can I say "no" to that?).

Thanks again, staigermanus!