Photoshop :: Anti-alias Graphic Using Transparency?

concerning anti-aliasing a graphic. Im currently using Photoshop CS2 running on Windows XP.

I have a graphic that I want to use with backgrounds of different solid colors and even the occasional multi-colored background. I want to smooth out the jaggies of the graphic in such a way that the smoothed graphic can be placed on a separate layer and the desired background can be inserted on a layer below.

I can successfully import an anti-aliased graphic IF I import the graphic and its background at the same time. But then the anti-aliased graphic is suitable for use only with that particular color background. I would like to eliminate this extra step if possible.

Suppose the graphic were black on a white background. The anti-alias pixels might be 75% gray, 50% gray, and 25% gray. Conceptually, it doesnt seem like it should be all that difficult for the anti-alias pixels to be black at 75% transparency, black at 50% transparency, and black at 25% transparency. Then, in theory, wouldnt this type of transparency anti-aliasing work for any color background placed underneath it? Is this possible in Photoshop CS2? If not, is it possible in a later version (might be a good reason to upgrade)?