For comparative analysis, I'll post up what I have personally written on the subject, when my damn computer works.
Police type operation? Please- we need units that work in anti (proactive) terrorism. That means getting the drop on an attack before it happens, then shooting, looting, and scooting. What we are skilled in now is counter (reactive) terrorism techniques, but all too often the chain of command and the bureaucratic turf wars render it less effective than is possible.
As for Fallujah? Police-type operation in my mind (as far as that city goes) involves full mounted patrols with enough small-arms to make the city of Darra look like California. Constant patrols will bring on new leads with the insurgency, but ultimately our mindset, or the mindset of fundamentalists, or both, must change before the situation resolves itself enough for us to pull out with relative peace of mind.
In truth, it resembles what I've done, including very few new ideas, more examples, and geared toward a military audience, instead of mine, based largely on a military audience with more attention paid to making civvies understand the situation.
Read my sig and you'll understand just how much respect I have for the politics that intertwine the military system. One of the key theses of "Self Perpetuating Destruction" (posted here) is to eliminate the political gray area.