-- It's a hot July morning, and we're skittering over the rooftops of the city in a Black Hawk helicopter. Lt. Gen. David Petraeus is gazing across miles of sand-colored houses bleaching in the sun, searching for evidence that some kind of order is returning to Iraq.

Petraeus points to the crisp, white frames of schools that America has rebuilt over the past year, to the short lines at gas stations, to the yellow trucks hauling Iraqi wheat to a refurbished grain elevator, to streets swept clean of debris so that roadside bombs can't be concealed so easily.

"I'm looking for indications of normality," Petraeus says over the roar of the helicopter. "It's what gets people productive again." We're visiting commanders of three battalions of an elite new "Intervention Force" that Petraeus is helping to create. The force will eventually have about 6,500 Iraqi soldiers who can move quickly to suppress insurgencies in urban areas, part of an overall army of about 70,000. Because their duty will be more hazardous, the members of this elite force will get about $100 more a month.

The new counterinsurgency force is one of the most important projects in Petraeus's mission to build a strong army and police that can stabilize Iraq -- and allow American troops to withdraw. Petraeus believes in this with a soldier's passion, but he knows it won't be real until it has been tested in battle.

Military analysts talk about "standing up" a new army as if it's as simple as placing toy soldiers on a board. But as the helicopter churns over Baghdad, Petraeus likens the process of military mobilization to moving a herd of cattle across a range. There are so many people and logistics, so many parts that have to be assembled, so many things that could go wrong. All a military leader can do is put the pieces in place . . . and wait.

And exhort. As he meets with each of the Iraqi battalion commanders, Petraeus repeats the same list of soldierly advice: They must share "best practices" with other commanders; they must gain the confidence of local tribal and religious leaders; they should never stop training their soldiers; they should remember that a good army serves the people, not vice versa.

Some of his admonitions may sound corny, but the Iraqis listen intently. "A tired soldier is a proud soldier." "The loyalty of your soldiers must be to their new tribe -- the military tribe." "I expect you to lead from the front in everything you do, except going through the chow line." He closes by telling each: "I look forward to going on patrol with you."

Certainly this looks more like a real Iraqi army than three previous efforts by the U.S.-led coalition that I visited over the past year. The officers have decades of experience in the old Iraqi army; many of them seem to be good leaders who try to inspire their men rather than browbeat them. And it helps, too, that since June 28, the army has been part of a sovereign Iraqi government. The Iraqi officers can now describe Petraeus and the other Americans as advisers rather than occupiers.

Lt. Col. Ali Malekey has just arrived at the Intervention Force's training camp at Taji, just north of Baghdad. He's an enthusiastic soldier who rattles off U.S.-style statistics on his battalion's readiness: ambush preparation, 60 percent ready; convoy protection, 70 percent ready. Malekey's most encouraging news is that many of his ex-officer friends are now asking how they can get into the new army.

In another barracks at Taji, Lt. Col. Safeen Abdul-Majid is preparing to deploy his battalion to southeast Baghdad in a few days. When I ask if he's sure that his troops won't run from battle, as some Iraqi units did during the uprising in April, he gives me a steely look. "I see in the faces of my soldiers the determination to fight and defend Iraq."

Finally we visit a base in southern Baghdad where the first of these battalions was deployed a few weeks ago. They've now been mortared and ambushed, and they're holding their ground. Indeed, they have responsibility for securing their small zone of the city. I ask the battalion commander, Col. Mohammed Ali Hussein, if he's ready for a real fight. "I am sure of my soldiers, and I'm sure they won't run away," he says.

All Petraeus can do now is move the guns, uniforms, advisers and Iraqi soldiers into place -- and be patient. He knows how much is riding on these soldiers, for Iraq and for America. But nobody can be sure the mission will succeed until they take their first shots.

davidignatius@washpost.com