re: What alternative do you suggest?
You make a good point, but it's becoming painfully and fatally obvious that every tiny bit of slack we cut the inhabitants of Fallujah results in the insurgents regrouping, resupplying, and mounting further attacks, even under the cease-fire.
As we have seen and heard in the past, kindness or forbearance on the part of our military is considered stupid weakness by our enemies.
If we are going to take this approach, risking the lives of American troops instead of simply obliterating the resistance, then it might be appropriate to consider this as a balancing factor when discussing our casualty count.