I've set Compiz as my window manager since all the other options were causing screen tearing. The problem is that this causes the title bar of the active window (even if fullscreen) to be completely transparent (but only in some themes), which I find incredibly annoying, since I can see the names and icons of other open windows behind it. This doesn't happen with any of the other window manager choices in MATE tweak.
Edit: The suggested question is asking about the menubar in GNOME, while I'm asking about the title bar of a single window in MATE.