The Strategy Page offers some fine insight into American/Iraqi strategy for dealing with the insurgency in general and for Fallujah in particular. A few excerpts:
During the April, 2003 invasion, Saddam's enforcers began to flee back to the Sunni Arab homeland, north and west of Baghdad. Those that didn't flee at the sight of advancing American troops, soon left when they realized that the Shia Arabs and Kurds were now hunting down enforcers. By the end of 2003, nearly all of Saddam's thugs were back in places like Fallujah. There, tribal chiefs, long on Saddam's payroll, soon found themselves in the company of many heavily armed Saddam supporters. Guess who started calling the shots? The Baath Party had a plan for what to do if the country were overrun and occupied by an enemy (most likely Iran, but the United States was a possibility as well.) Baath had money, and people who knew how to do terror.
Baath Party operators had been working with criminal gangs, running criminal operations (officially sanctioned, or on the side) and terrorizing the population for decades. The Baath people also knew they had an edge over the Americans, as Baath could, and had, done whatever they wanted to get their way. The Americans, for all their nifty weapons and gadgets, had to operate according to rules of conduct. American troops could not kidnap people to get their children or siblings to carry out attacks. The Americans could not summarily execute anyone who failed in a mission, or refused to do what was asked.
But the Baath Party plan didn't work exactly as expected. The Americans were aggressively recruiting and training new Iraqi security forces. This had to be done from scratch, since no one but Saddam loyalists worked security while Saddam was in power, and all those people were Sunni Arabs whose loyalty was now questionable. But the new government, and coalition police and security experts, persevered. Trying to work out deals with the tribal chiefs didn't work, mainly because Baath and al Qaeda threatened to kill any chief that made peace with the government.
So the government began to shut down the "little Fallujahs" around Baghdad. This was good practice for the Iraqi troops and police. The Iraqis would need all the practice they could get before taking on Fallujah, for that's where those who escaped the Iraqi dragnet, in places like Samarra and many other smaller towns, run to. While the Iraqi and American units flush the thugs out, Fallujah itself is being hit with smart bombs and raids in the suburbs by ground troops.
Sometime before the end of the year, Fallujah will fall, and the Baath Party enforcers, and the al Qaeda terrorists will have to scatter. That will make the bad guys more vulnerable, and less effective. That, of course, is the objective.
The wild card in this prediction, of course, is how much patience the American people have to see this task through to the end. We'll know the answer to that on November 3rd.