Thanks everyone. I found the problem. It sort of had to do with the atmosphere as Peggy suggested. It wasn't the atmosphere directly, but a huge metacloud that was over the image to make it dark and fuzzy. When I removed the metacloud, everything was fine. I had tried another alpha plane, one I created, and it, too, had the box around it when the metacloud was present.

I wonder why the metacloud caused the problem with the alpha planes. Any ideas?