To the best of my knowledge, the right direction would be to start by subscribing to these bugs, all of which are potentially related to compiz stuttering...
Bug 888039: Compiz performance degrades (begins stuttering) over time
Bug 861061: [regression] Unity makes 3D apps run much slower:
Actually, Unity makes all apps stutter and slow. It's mostly noticeable in 3D apps where you care about and often measure framerates.
Bug 880707: [regression] Visible tearing occurs even when "Sync To VBlank" is enabled, but only when Unity is active:
It might not sound related, but the fix we're working on for 880707 should reduce stuttering and improve compiz performance in general.