[Wine] Problems with compiz, fglrx, and City of Heroes

[spicycat]

I just upgraded my video card from an 8800GT to a Radeon HD 5770.  I've got the proprietary 'fglrx' driver installed.  I am using Compiz/Emerald as my window manager and compositor, with the desktop cube enabled.

When I launch City of Heroes full-screen and then try to rotate the cube via hotkey the cube rotates to a new face and immediately repaints City of Heroes over the top of it.  The game won't accept any input unless I'm rotated onto the correct face of the cube, but it paints itself over all of them.  How can I stop this from happening?