By Tuesday, the United States will have withdrawn its combat troops, with few exceptions, from Iraqi cities, in accordance with a security agreement with Iraqis signed in November. (All U.S. troops are supposed to be out by the end of 2011.)

During my last trip to Iraq, in December, it was hard to imagine that this large-scale shift of men and equipment could be completed in such a short time. However, as Gen. David Petraeus told me in an interview, "The process of removing our combat bases from cities is on track and will meet the deadline." Quite impressive.

Clearly, many Iraqi players will try to use the pullout to advance their own agendas. Prime Minister Nouri al-Maliki, with an eye toward the January 2010 elections, is calling it a "great victory" against occupation. Others are hoping to restart civil war: A wave of lethal bomb blasts in Shiite neighborhoods last week killed about 200 people. (Violence overall is still way down, but these bombings stoke fearful memories.)

So the big question is, what happens next? In my phone conversations with several Iraqis, each said the pullback would spur new violence. Many shadowy groups - from al-Qaeda fragments to Iranian agents to mafiosi - will test the ability of the Iraqis to take on more of the security burden.

"We have been concerned by the sensational attacks carried out by those trying to revive sectarian violence," Petraeus said. "Beyond that, there will be those who want to attack in order to say they forced the withdrawal." He added, "We don't think that will get much traction, because Iraqis are well-aware the pullout . . . is part of the implementation of the U.S.-Iraqi security agreement."

The good news is that spurts of violence are unlikely to rekindle full-scale sectarian warfare. Sunnis have been chastened, and Shiites no longer fear the old Sunni order will be restored. "We've had a bellyful of that bloody fighting," one Sunni resident of Baghdad told me, "and no one wants to return to that."

Moreover, some U.S. troops (the number hasn't been made public) will stay in cities as trainers and advisers. "There is an agreement reached for the establishment of coordination centers that will remain in Baghdad, Mosul, and Basra," Petraeus said, "and will allow U.S. forces to share information, coordinate activities, and, if required, provide U.S. enablers to assist Iraqi forces."

Teams of advisers partnered with Iraqi units will also remain, Petraeus added, to ensure sharing of intelligence, coordination of operations outside cities, and access to requested assistance.

If you think this means little has changed, think again. The change is dramatic. The closure of urban U.S. bases and outposts is already affecting security in cities, say Iraqi journalists and sources in Baghdad, Fallujah, and elsewhere.

Iraqi army troops and police don't go out on patrol as U.S. forces did, which means they have less contact with the population and get fewer tips about bad guys. This makes it easier for criminals to operate, along with other disruptive forces.

In mixed areas, Sunnis still fear the Shiite-dominated security forces are biased. Even in Sunni Anbar province, where the police are all Sunni and violence has plummeted, the U.S. pullback has been accompanied by an uptick in roadside bombs, maiming locals. The perpetrators may want to convince Iraqis that their current system cannot work.

A source in Fallujah told me that, even though most locals want the Americans to go, they are nervous. Al-Qaeda elements still lurk, and the police are corrupt and hapless. "People don't know whom to follow," the source told me.

U.S. officials are hoping Iraq's political leaders will tamp down renewed sectarian violence or any flare-ups between Kurds and Arabs in the north. Much will depend on the performance of Prime Minister Maliki, who built support by taking credit for the sharp decline in violence since 2006 and 2007.

Yet Maliki's sense of his abilities is inflated. His most touted achievement - last year's crackdown on radical Shiite militias in Basra - required U.S. forces to rescue his beleaguered troops. Much will depend on his private grasp of reality, irrespective of his public showmanship.

However - and this may shock many Americans - Maliki has garnered popularity (while rousing some opposition) by presenting himself as a strongman who isn't above cracking heads. Many Iraqis tell me their tribal society will ultimately veer back toward "another Saddam who is a little better."

Maliki may ride the current violence to become that strongman, albeit one chosen by ballot. Or Iraqis may turn against him if he cannot restore security and services. At any rate, Iraq is likely to limp along, making - let's hope - slow progress.

And, by the way, there is another deadline looming: the end of July, when Iraqis are supposed to hold a referendum on the entire U.S.-Iraqi security agreement. A "no" vote would compel U.S. forces to leave before the end of 2011.

But Iraqi political sources tell me the referendum will probably be delayed to coincide with the January elections. Even Iraqi nationalists fear that too swift a U.S. withdrawal will boomerang.