U.S. military commanders here are calling it Operation New Dawn.

Starting July 1, with the transfer of limited sovereignty to Iraqi authorities, military helicopters will switch to flying "friendly approaches" instead of menacing ones, U.S. soldiers will go on patrol only when accompanying Iraqi security forces, and any shooting of U.S. weapons meant to harass or interdict will require higher-level approval than before, military officers here said.

In Mosul, Army Brig. Gen. Carter Ham, who leads a brigade of armored Stryker vehicles and other forces, said he expected that his troops would assume a much lower profile.

"On July 1, what I want Iraqi people to say is: 'Where are the airplanes? Where are the Strykers?' " Ham said last week. "What they'll see instead will be Iraqi forces."

For U.S. troops in Iraq, the coming political change -- from occupying power to supporting partner -- is supposed to be accompanied by a major shift in military mission and tactics. While legally still authorized under a U.N. resolution to use "all necessary means" to ensure security in Iraq, U.S. commanders say they intend to reduce combat operations, concentrate on training and assisting Iraqi forces, and promote local governance and economic development.

U.S. and Iraqi officials acknowledged in interviews and in briefings to Deputy Defense Secretary Paul D. Wolfowitz last week that their plan was sure to be complicated by two main factors.

First, many of the 215,000 members of Iraq's fledgling forces are far from ready to take over much of the security burden. And second, the deadly insurgency that emerged shortly after the U.S.-led invasion last year continues to bring fresh waves of violence, most recently a surge of assassinations and attacks on oil facilities.

Under such uncertain circumstances, U.S. military authorities are trying to show at least their willingness to step back and let Iraqi forces take the lead, but are hedging their bets by keeping U.S. troop levels at around 140,000 and girding for a gradual turnover of operational responsibility.

"If Americans are in danger, if there's a really bad person we've got to go after, it's the same old rules," Wolfowitz told reporters traveling with him, making clear that U.S. forces had no intention of withdrawing from the fight. "But we would like people to see that something has changed. In the first few weeks, a lot of the challenge is how to create some optics when the underlying substance hasn't changed that much."

At the headquarters here of the 1st Infantry Division, Maj. Gen. John Batiste and his staff showed Wolfowitz a timeline last week that charted two lines through February. One line, which fell gradually across the page, represented the U.S. military profile; the other, which rose steadily, represented the Iraqi security services.

The lines intersected in September, which is when Batiste said he estimates that Iraqi forces will be able to take full charge of combat operations and policing in the region. By January, when national elections are scheduled, he is counting on Iraqi forces to be completely responsible for securing voting facilities, he said.

Commanders here and at other bases throughout Iraq offered assurances last week that recently intensified efforts to train and equip the Iraqi forces were beginning to bear fruit. Vehicles, communications gear and other equipment for the new forces that had been in short supply have begun to flow in. Recruits are being better vetted. Authorities are placing greater emphasis on ensuring the quality of the forces rather than their quantity.

The commanders also provided accounts of insurgent cells being uncovered and broken up, of public works projects being advanced and of Iraqis coming forward with crucial tips about the location of roadside bombs.

"This is the theme of this briefing: Glass is half full, things are headed in the right direction," one senior commander told Wolfowitz.

But the commanders also said there were signs for worry, particularly regarding the continued strength of the insurgency. For instance, in Baghdad's Sadr City neighborhood, which has been a center of resistance to the U.S. occupation, the number of insurgent fighters was reported by U.S. military authorities to be largely unchanged despite the deaths of hundreds in battles since April. The dead have been replaced by other fighters, many of them teenagers, U.S. authorities said.

Commanders also warned that U.S. forces were being spread thin. In the northern city of Mosul, military authorities noted that roadside bomb attacks rose after some U.S. troops were sent south for other duty, as the drop in the American presence allowed insurgents more time to plant the bombs.

Iraq's long borders with Syria and Iran also remain largely uncontrolled because of a shortage of patrols, according to U.S. commanders in Mosul and Tikrit.

"I'm stretched about as thin as I'd want to be with 22,000 troops," a senior officer told Wolfowitz in a briefing attended by reporters on the condition that names not be cited.

Lt. Gen. Thomas Metz, the second-ranking commander of U.S. forces in Iraq, acknowledged that as U.S. forces shift to more supporting tasks in Iraq, such as training Iraqi forces and protecting leaders of the new interim government, they will be even more hard-pressed to muster troops to conduct combat operations.

"By the time you put troops to task, the troops available to do offensive actions are less," Metz told reporters in an interview last week.

Still, Metz rejected the idea that more U.S. troops should be sent to Iraq. Instead, he said, greater efforts would be made -- through improved intelligence-gathering and other means -- to use available troops more efficiently.

The shortfall that appeared to concern Wolfowitz the most was not in troops but in the money that U.S. commanders have used to pay for schools, hospitals and other smaller-scale local projects that have improved community services and fostered goodwill. The funds, known as the Commander's Emergency Response Program (CERP), have been parceled out by the Coalition Provisional Authority, which ceases to exist with the transfer of sovereignty.

Wolfowitz said Iraq's interim prime minister, Ayad Allawi, had expressed a willingness to provide "bridge funds" for "CERP-like" projects.

The offer was indicative of the kind of cooperation that U.S. and Iraqi authorities said would be needed for the next phase of relations to work smoothly, replacing the days when U.S. commanders could operate unilaterally.

Pfc. Adam Krum of the 1st Marine Division mans a Humvee-mounted TOW missile during a mission near Fallujah.