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But a majority of the military presence on the streets is Iraqi.

From the moment motorists drive through the huge arch at the city’s northern entrance, they are confronted with a ragtag but daunting collection of armored police vehicles, Iraqi Army Humvees, cold war-era tanks, pickup trucks with turret-mounted machine guns and bullet-riddled personnel carriers.

Canal bridges are guarded by head-high steel pyramids, from which soldiers observe bustling markets through a bulletproof window.

Maj. Tom Holloway, a British military spokesman, conceded that the Iraqis would have “struggled” without the warplanes available to coalition forces. But he said: “I don’t think it’s a crutch. I think they would have tackled it in their own way and possibly, probably, achieved the same result.”

And the result, whoever is ultimately responsible, is in many ways remarkable.

At the College of Fine Arts, female students said they felt more, but not entirely, free to wear the clothes they liked.

“I used to be challenged for what I wear,” said Athari, a 19-year-old student wearing heavy makeup and a bright orange headscarf pushed high back on her head in the liberal fashion disapproved of by Islamic radicals. “Makeup was forbidden; short skirts were forbidden. I will not mention their name, but they were extremists. They are still here, but quieter now.”

Qais, a music student, spoke of his relief at no longer having to hide his violin in a sack of rice in his trunk.

Most of the students were Shiite, but one youth named Alaa said that he was a Sunni and that 95 percent of his relatives had fled Basra after sectarian killings, including that of his uncle. “I want to thank Mr. Nuri al-Maliki, because he cleaned Basra of murderers, hijackers and thieves,” Alaa said.

It was not an uncommon sentiment. In his city center office, Yahya, a wealthy businessman said he had just begun going onto the streets without his customary 10 bodyguards. Insisting that he was not a political supporter of the prime minister, he said he was nevertheless so grateful for the security improvements that he and colleagues had downloaded Mr. Maliki’s face onto their mobile telephones as screensavers.

But as with the American-led surge in Baghdad, there are abiding uncertainties.

These center on how long such a heavy military presence can be sustained on urban streets, and what happens when it departs.

Gen. Mohan al-Freiji, the Iraqi commander in Basra, said the city was “75 percent” under control. He said the principal threat stemmed from rogue elements of the Mahdi Army and factions like the Iraqi Hezbollah (Party of God), Thairallah (Revenge of God) and Fadhila (Virtue).

Emphasizing the urgent need to address decades of poverty and neglect, he said the government had to provide jobs and investment to convert short-term military gains into long-term political and economic ones.

“This is a city which sits on top of oil, but its young people are unemployed,” he said.

Sadrists protest that the Basra operation is a cynical exercise to weaken Mr. Maliki’s Shiite rivals ahead of provincial elections in the fall.

At Friday prayers in Kufa last week, the Sadrist preacher, Sheik Abdul Hadi al-Muhamadawi, said, “There is a large-scale conspiracy to remove the Sadr movement from the government’s way by all means, because it refuses the presence of the occupier in Iraq.”

Such words underscore the widespread belief here that the Mahdi army has its own reasons for lying low and is by no means eliminated.

During one Iraqi Army patrol in Hayyaniyah at dusk, the soldiers, elsewhere relaxed, became jittery. Belying the local commander’s insistence that the Sadrist stronghold was “90 percent or more secure,” some pulled up face masks that they had not worn in other districts. They also fired bullets into the air at the slightest delay in traffic, an aggression unlikely to endear them in an area that, although calm, was noticeably less welcoming.

Haider, a policeman at a checkpoint outside the Sadrists’ former headquarters, said his family had been threatened, even at his home in the capital.

“I have spent 60 days in Basra and haven’t been home to Baghdad,” he said. “I will be killed if I go now. My family have received dozens of fliers with threats from the Mahdi Army.”

Nevertheless he, like many others, said the evacuation of the factions from their once-untouchable headquarters had brought about a psychological shift. Outside the Sadr office, Iraqi soldiers now sit atop the roof, their tripod-mounted machine guns overlooking the tin-roofed Sadrist prayer hall, which lies half-demolished.

“The Mahdi Army used to use this office like the Baathists when they were The Party,” Haider said. “They were ruling like the government of a state. They stopped police doing their duty, from implementing the law.”

Noting that the Baath Party of Saddam Hussein, once much stronger than the Mahdi Army, had been routed, he said, “The Mahdi Army will meet the same fate exactly, and worse.”

Yet traces of the old order remain. One wall in central Basra still bore the unsigned scrawl: “We warn girls not to put on makeup and to wear scarves. Anyone who does not follow these orders will be killed.”

Stephen Farrell and Ammar Karim reported from Basra. Iraqi employees of The New York Times contributed reporting from Basra and Kufa.