curving graphics (similar to text along path)

I am trying to make a CD cover graphic in photoshop.

I have a logo that has been flattened, and it is a standard rectangular shape. It would flow with the shape of the CD much better if I were able to apply a curve to it, similar to using the text tool along a curved path.

I have used the Transform tool which only allows changes in angles. I have also tried multiple filters...
Filter --> Distort --> Pinch
Filter --> Distort --> Polar Coord
Filter --> Distort --> Spherize

and none of these give me the desired FX. They only massacre the image.

Without redrawing the logo from scratch, is there any way to bend the graphic along this curve?

Thanks,
FH

To really pull this off you are going to need a vector program like Illustrator. But if you are using square pixel graphics, it will indeed stretch them, and I don't think there is a way around it.