What kind of fighting will occur in Fallujah? It will be a game of wits, as well as weapons. The most professional and experienced anti-government gunmen are in Fallujah, and they have developed many countermeasures for the coalition advantages. A major disadvantage is the coalition control of the air, and the constant presence of UAVs, aircraft or helicopters. Too many gunmen have seen their buddies ambushed, or jumped by unexpected coalition troops, to ignore the possibility of a UAV above sending live video of the battlefield to coalition commanders. So the gunmen try to set up movement routes that cannot be seen from the air. Rugs or sheets are spread across alleys to make this possible, and sometimes even short tunnels are dug. The downside of this is that movement is inhibited. In fact, American troops do not always have a vidcam equipped UAV over the battlefield. But Department of Defense public affairs people like to distribute videos of such operations. The implication that American troops can "see everything" is meant to intimidate the enemy. It does, and slows down enemy movements, often fatally so.
In any event, the loose cordon around Fallujah has made it possible for many Sunni Arab gunmen to flee Fallujah. The gang leaders will probably not stay to fight, but with Fallujah gone, a major hiding place for these guys is under government control. The fewer places where the gangs can gather openly, the fewer gangs can operate, and the fewer Sunni suicide bombers and gunmen there are in action.