Lt. Col. Jim Rainey describes the battle here as "tackle football in the hallway, with no roof on the hallway." It's an apt analogy for urban warfare in sometimes extremely close quarters.

But after 21 days of merciless battering by U.S. weapons, parts of Najaf have very nearly no hallway at all. Grand Ayatollah Ali Sistani, the most influential Shiite cleric in Iraq, negotiated a cease-fire Thursday, but not before parts of Najaf had been devastated.

Pinpoint fire and tight restrictions on munitions ensure that the gold-domed Imam Ali shrine remained all but unscathed. But the core of the city around it, a destination of longing for millions of Shiite Muslims, is so mauled that American commanders debate which famously ruined wartime cityscape Najaf now resembles most.

"It's like Stalingrad," a senior 5th Cavalry officer said.

"Sarajevo," Rainey maintained.

"Beirut," a Marine commander said.

"Not Dresden," an Army field officer said while standing watch at a panorama of blackened, half-destroyed buildings a few dozen yards north of the glittering shrine. "Not enough fire."

The damage to Najaf is the consequence of an urban setting for battle, a woefully overmatched enemy and an American military doctrine that unites terrifying firepower with almost zero tolerance for casualties in its own ranks.

"If we take fire from it, we destroy the whole building," an Army commander said Thursday, after he ordered junior officers in his headquarters to do just that, once they received clearance, against a structure the Mahdi Army militia, the enemy here, was using as a firebase.

The staff had a broad assortment of weapons available at the other end of their radio handsets: the Marines' 155mm howitzers just behind the headquarters, Apache helicopter gunships on alert or swooping menacingly over the battlefield and a fighter-bomber on station at 10,000 feet.

At one point this week, soldiers from a 1st Cavalry Division battalion led by M1-A1 Abrams tanks and heavily armored Bradley Fighting Vehicles watched in bemused wonder as their opponent sent a donkey with a rocket-propelled grenade strapped to its side onto the field of battle. The remote triggering device was a string running toward the building corner from which the animal had emerged.

"We actually had reports of 'engage and destroy the donkey,' " said Maj. Tim Karcher of the 7th Cavalry Regiment. The animal appears to have died as another enemy casualty.

The 7th Cav, once led by Gen. George Custer at Little Big Horn, has fared better in Najaf. Since arriving from north of Baghdad and setting up a cordon around a large section of the city south of the shrine, the unit's 2nd Battalion has fought almost nonstop for two weeks without losing a single soldier.

Perhaps the closest call came this week, when a grenade exploded in a basement room where Sgt. Varitogi Taetulli was wrestling an insurgent. The fight was a miniature version of the larger battle: Taetulli, from American Samoa, weighs 230 pounds. The militiaman weighed perhaps half as much.

But the crucial advantage was that Taetulli was wearing an armored vest. He escaped the grenade explosion alive and hollering to get back in the fight. The militiaman died immediately.

"It's the best feeling in the world," Karcher said of the armor, technology and munitions that safeguard the U.S. force. "We've been given the best tools in the world for waging war."

The battle for Najaf has been a study in the urban warfare that conventional wisdom says can only cause high American casualties. That is what U.S. invasion planners feared -- and subordinates of deposed president Saddam Hussein promised -- would occur last year in a protracted fight for Baghdad that never came.

Officers of the 7th Cavalry said their experience over the past two weeks found such fears exaggerated. So far, 11 Americans have died in the fighting; Iraqi health officials say that hundreds of militiamen and other people have lost their lives.

The 2nd Battalion was told to tighten the armored cordon around Najaf's old city, moving more than a mile through dense residential neighborhoods where Mahdi Army irregulars had enjoyed free rein.

But there was little house-to-house fighting, officers said. Maj. Scott Jackson, the 2nd Battalion's executive officer, described U.S. forces advancing using a kind of citified version of the island-hopping strategy used in World War II in the Pacific, attacking the militia at its strong points and establishing strong points of its own, then dominating the surrounding terrain. Tanks were very useful.

One strong point was tall buildings, which offered platforms for scores of American snipers. Precision fire was a must, given the bar imposed on firing heavy guns toward the shrine.

The other strong point was schools. Militiamen found them convenient places to store arms and mount defenses. The 7th Cavalry took four on their march toward the shrine complex, in some cases shelling schoolhouses that other U.S. forces had boasted of rehabilitating as part of Iraq's reconstruction.

One recent day, at the forward-most school the U.S. soldiers had occupied, a heavy machine gun was mounted on a child's desk and an orange banner hung from a second-story window to warn pilots against bombing the school by mistake.

At the same time, the 7th Cavalry made efforts to show goodwill to residents who stuck it out through the fighting. More than once, medics set up a mobile clinic to treat Najafis, while soldiers handed out food -- pre-packaged chicken and beef dishes labeled in Arabic as halal, or approved for the Muslim diet.

"The way you defeat an insurgency is by co-opting the population," Jackson said. "You don't end an insurgency by leveling the city."

And yet, when the 7th Cavalry arrived at the road that rings the shrine's immediate neighborhood like a moat, it let loose a furious barrage. Multi-story buildings at the main intersection of the ring road crumbled under the Americans' combined-weapons warfare -- bombs and missiles from the skies, shells from distant artillery, direct fire from the 25mm chain guns of Bradley Fighting Vehicles and the 120mm cannons of tanks.

The intersection that pilgrims approach immediately before sighting the splendid shrine is now a hellish landscape of standing water, Swiss cheese walls and ruined hotels.

Less than a mile away, the northern approach to the shrine is battle-savaged as well, framed by a bent metal banner proclaiming that in the end only God will be alive.

"We are destroying this city," a Marine officer said with a sigh at one point in the battle, described by some locals as a siege.

How the Arab world sees the damage is a question that field commanders said they had little time to ask themselves as they constantly changed battle plans. Several noted it was Sadr who brought the fight to the holy city, not them.

Field commanders add that key decisions on what to attack in the city, and how strongly, were made by senior officials in the U.S. command and Iraq's interim government. The Iraqis, who saw the militia takeover of Najaf as the most severe test to date of its new authority, had the ultimate say, the Americans say.

But it would not hurt, one officer said, to announce reconstruction plans right away. If the destruction "is the price of shoring up the Iraqi government, then okay," one U.S. commander said while standing in the ruins. "But it probably wouldn't hurt if we found a way to make things right here."

A 7th Cavalry Regiment soldier stands ready near the remains of Najaf's main road around the holy shrine of Imam Ali.