I'm using both Compiz and Gnome-Do on my LMDE vb install using MATE.
There was a conflict with Compiz and Metacity causing high CPU usage which I was able to fix based on this:viewtopic.php?f=190&t=99051
basically, in terminal run mateconf-editor and go to desktop>mate>session>required_components and change the windowmanager from marco to compiz.
I'm not sure if that will solve what problem you are having, but it did bring my CPU usage down to normal and I've had a stable system since.
If this doesn't solve your problem, please describe your symptoms in more detail.