What's the problem - black video screen, crashing desktop or what?
I haven't noticed any trouble doing anything (even playing games) while running Compiz and having all the irrelevant stuff going on at the desktop, except for occational crashes, titlebars getting lost without reason etc., but those are merely what you get when trying to make it look too good
Compiz is nothing perfect - it has problems - and it certainly doesn't work well with all hardware+driver-combinations. If it's difficult, get rid of it (simple).
I suggest trying out different video drivers or video hardware, or different Compiz(-Fusion) version. Note that if I'm not mistaken, CompizFusion is what you ought to be talking about, not plain Compiz anymore.