Photoshop :: How To Remove Fringe Around Picture?

I created an image for a programming project with Photoshop. When my application runs, everything that is red is drawn as transparent when the form is rendered. The purpose of this is to make an application with a shaped form instead of the regular rectangular windows.

Anyways, my problem is with the image itself: there is a little fringe around it. I am no Photoshop expert, but it appears that the fringe is created by Photoshop when my image is rendered against the red background I created. My image, let's say a circle, is actually in a separate layer, and the background layer is red all over. What happens is that pixels, let's say blue, near the edge of the circle in the image layer turn to purple to smooth out the circonference of the circle in some sort of anti-aliasing fashion.

Since at runtime the red disappears, I end up with a purpleish fringe around my circle, which is annoying. I tried using a different background colour, but I still end up with a little fringe, just of another colour. I tried the various "defringe" options of Photoshop but without any success.