I don't have much experience with ATI graphics cards, but my nVIDIA card has an option called "resize HD desktop" or something like that under the advanced controls. When you select that option it presents you a big blue screen (full screen) with a thin yellow border and yellow arrows pointing to the exact corners. In the middle are two sliders, one for horizontal and one for vertical. The sliders allow you to squeeze the display vertically and/or horizontally independently to make it fit your screen perfectly.
I use this capability on my projector, because for any "normal" 1080p source I have the projector zoomed just a little bit into the black border around the screen. For a computer this doesn't work well as my start menu and the top of some programs wind up in the border. With the nVIDIA tool I just dragged the vertical slider a bit until the image fit the screen and pressed save.
What it really does behind the scenes is create you a new resolution, as has been previously suggested, but it's all hidden from the user so you don't have to know or care that that's what it's doing. I think my resolution wound up at something like 1920x1040 or give or take a little after squeezing in the start menu. The projector itself though is getting a standard 1080p signal from the video card, so it doesn't know the difference.
I have no idea if ATI has a similar capability on their cards, but if not you should still be able to type in a "custom resolution" in the CCC and see if the card/display can handle it. Best of luck!