If the folks running this operation (on our side, I mean) know what they're doing, they'll have AC-130 gunships circling 24/7, and every time any building Fallujah shows armed resistance, a storm of metal will descend from the sky within seconds and disintegrate the place. Time for another lesson of "shock and awe", up close and personal.
And while gathering links for the above pictures, I found this amusing AC-130 crew patch:
