THAT is the $64,000 question. We may be able to exercise a certain level of control over Falluja by bullying the Iraqi gendarmes into doing our bidding. That may be sufficient for the task at hand, which is < cue the chorus > putting an "Iraqi Face" on the problem until real power transfer takes place.
But everyone is missing part of the point: we have SLAUGHTERED these fighters in Karbala and Najaf, and word gets out! It forced the Karbala "militia" to basically give up and agree to our terms. Al-Sadr is being told by all his fellow Najaf-ians to get the hell out. This has an effect in Fallujah, believe me.