I used Compiz with LMDE with GNOME 2 since starting to use LMDE.
With update pack 4, the choices of window managers has changed with GNOME 2 being replaced with GNOME 3, Cinnamon and MATE (fork of GNOME 2). I tried Cinnamon for a while, and yes it is indeed impressive, it is still too early to start using it to replace Compiz w/ GNOME 2.
To get Compiz working with MATE, there is one additional issue than with GNOME 2. With GNOME 2, you can simply run "compiz --replace" to activate Compiz. In MATE, this works, but then then some MATE processes end up pegging the CPU high (constant running 50% CPU on a dual core -- I would assume this would be 100% on a single core system or 25% on a quad core system). To stop the CPU from running high, you run a "killall -9 marco" after activating Compiz. However, as I found, it doesn't seem to work very well from a script. I've always had "compiz --replace" as a startup script in "Startup Application", but simply adding the kill directly after didn't seem to have the desired effect. Even when ensuring Compiz was starting up as a background process with a &, the killall immediately after still didn't appear to be having any effect. I also tried putting a sleep inbetween steps.
The ultimate solution is to prevent the marco from starting completely.
With that said, here is the ultimate workaround to get Mate with Compiz running as your desired Window Manager.
First, you will need to install mateconf-editor (sudo apt-get install mateconf-editor). This will add a red-icon version of Configuration Editor to your Programs (not to be confused with gconf-editor which you may have previously installed as well). Start mateconf-editor from a terminal or from the Programs menu.
Second, navigate to /desktop/mate/session/required_components. Locate the windowmanager setting, and change it to either blank or compiz. I actually went with leaving it blank and continuing my prior tradition of having a "compiz --replace" execute via "Startup Applications", rather than changing the default to Compiz.
That's it. Now have fun with CompizConfig (ccsm) to edit and configure your Compiz environment.
If you don't have Compiz installed, install the components via Synaptic. I prefer to install all the plugins as well to fully customize Compiz. I use compiz-gtk, compiz-dev, libdecoation0, compiz-plugins, compiz-core, compiz-fusion-plugins-unsupported, libcompizconfig0, compizconfig-backendgconf, compiz-fusion-plugins-main, compiz-fusion-plugins-extra, compiz-fusion-bcop, and compizconfig-settings-manager.
