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Eyes peering through slits in black masks, the commandos creep up the floors of the Baghdad apartment building, ready to pounce. Their target is Omar Tamimi, an insurgent believed to have carried out the January assassination of the governor of Baghdad province. In the past, the responsibility for such high-profile operations has been shouldered by teams of elite U.S. troops. But on this night, the American commandos are playing a support role to members of the new Iraqi army's Counter Terrorism Task Force, a unit the U.S. is training to take on more counterinsurgent dirty work. The early stages of the operation unfold smoothly. One team of troops stops on the second floor, the other continues to the third, where they place explosive charges against a thin wooden apartment door. Two booms in quick succession echo in the concrete stairwell. The doors shatter inward in a storm of wooden splinters, and the Iraqi and American troops, identically outfitted with US-made M4 carbines, night-vision goggles, boots, uniforms and body armor, burst in.

Inside the troops find children and three women, one of them elderly, cowering on the floor. The Iraqi forces search the apartment and find three men. They turn up Tamimi's identification papers, but not the target himself. After cuffing the adults—including the women—with plastic ties, the Iraqi commander grills them about Tamimi, but gets nowhere. Then an Iraqi officer begins chatting with the children; before long one of them reveals that Tamimi had been in the apartment moments before the troops rushed in. "He's still here," the officer tells the Americans. Soon a Green Beret is heard yelling and laughing in the kitchen. Under the sink he'd kicked a thin wall. Behind it was Tamimi, a thin sketch of a man, curled into a ball.

Operations like the one that netted Tamimi earlier this year provide a glimpse of what U.S. commanders hope will be the future of combat in Iraq. Two years since the invasion of Iraq, the U.S. is scrambling to train and equip a new Iraqi army to take over combat duties and pave the way for a reduction in the size of the U.S. troop presence. After a slow start, the training program appears to be picking up momentum: last week the Pentagon announced plans to trim the number of U.S. troops in Iraq from 150,000 to 105,000 by early next year, a move that reflects the improved capabilities of the Iraqi forces. The top commander of U.S. ground forces in Iraq, Lt. Gen. John R. Vines, said that "very much sooner rather than later, Iraq will be able to provide for its own security."

The Iraqi special-ops units like the one that captured Tamimi are spearheading that push. TIME was recently granted access to the Iraqi commandos and their U.S. advisors, observed their training sessions and accompanied the units on patrol. While their numbers are few, Iraqi special forces have assumed a bigger role in sensitive counter-insurgent operations, often acting as the lead teams in raids and rescue missions. In some cases, Iraqi units have used intelligence gleaned from locals to identify their own low-level targets, and then execute small raids on their own. Trained by Task Force Pioneer, a unit drawn from a support company from the U.S. Special Operating Force's 10th Group, the emerging Iraqi commando units have impressed U.S. commanders with their combat performance and bolstered confidence that Iraqis can keep the insurgents at bay on their own. "We can step away more now," says the U.S. commander of Task Force Pioneer, who, like all of the special forces in this story, cannot be named. "It's about 50-50."

That said, the U.S. hasn't yet ceded command and control to the Iraqis. "We train the rank-and-file but we're the leadership," says the Pioneer commander. However well-trained, the Iraqi special forces comprise only a tiny fraction of the 57,000-member Iraqi army, which has been plagued by low morale, inconsistent training and infiltration by insurgents.

But the U.S. hopes the commandos provide a model for improvement. Over the past year the ISOF units have conducted 538 combat missions, capturing 431 suspected insurgents, over 1,700 weapons and tons of munitions. They've seen bloody action in the battles for Najaf, Samarra and Fallujah, and have fought insurgents in Ramadi and Baghdad. Among the Iraqis' biggest successes were the capture of militants involved in the April 2004 attack in Fallujah on four U.S. security contractors; and they killed an insurgent suspected of involvement in the beheading last May of American Nicholas Berg. Advisors from the U.S. Green Berets say the Iraqi special-ops teams have suffered none of the problems of desertion in the face of enemy fire seen in most of the regular Iraqi units. None have refused to fight, they say, and rates of those absent without leave are well below other forces. "It's unbelievable, but it's all down to the espirit de corps," says the Americans' Executive Officer.

Putting Iraqis on the front lines, U.S. officials say, is yielding results in the shadow war against the insurgents. When the key to unraveling insurgencies is denying the rebels the support of the population, putting an Iraqi face on the offensives is vital. It also helps avoid blunders. Often targeting information is slightly off, with troops raiding the wrong house. Local Iraqis are loath to point the Americans in the right direction. "They're not scared of Americans, but when an Iraqi in a ski mask confronts them they talk a lot more, and they're more likely to say, 'He's not here but lives across the road,'" says Task Force Pioneer's commander. During the raid on Tamimi's safehouse, the joint U.S.-Iraqi team hauled off Tamimi and another insurgent suspected of being a key bombmaker. The other men upstairs were left behind, a mark of the more "surgical" style of business the Green Berets are hoping the Iraqis can deliver them, blunting locals' perceptions of Americans as brutish and arbitrary. "In the past, we'd have scooped them all up," says an American with the CTF, "but we only took the guys our Iraqis said were dirty.

The Iraqi Special Forces Brigade, or ISOF, is made of two distinct parts. The 36th Commando Battalion, famed for its tenacity in battle, is a hard core of elite troops trained in urban combat and reconnaissance who are put through what their U.S. trainers dub "Ranger school-lite". Applicants for the 36th are carefully screened for criminal or insurgent connections. Many have past military experience. Under the Green Berets' tutelage they endure a three-week initial training course designed to elevate their fighting skills and build a cohesion even the veteran fighters have not known before. Their marksmanship drills make them far superior to their army colleagues. Comparing the U.S. regimen to those from his days in Saddam's army and later as a Kurdish peshmerga officer, the 36th Commando school commander says "the Americans' training kicks the Iraqis' ass".

The ISOF brigade's other component is the Counterterrorism Task Force, modeled on the U.S. Delta Force. With more intensive weapons training, and specialist skills such as fast-roping from helicopters, the CTF is more adept in the arts of close-quarter combat, like those needed when storming a house to rescue hostages. While the Commandos wear Iraqi uniforms and carry Belgian-made Kalashnikov knockoffs, the CTF members don U.S. fatigues, carry cut-down M-4 carbines, travel in armored Humvees rather than open-back trucks, have modern communications equipment and pack sniper rifles and heavy weapons such as AT-4 anti-tank missiles. When CTF soldiers queued on Jan. 30 at a Baghdad polling station to vote people confused them with their American counterparts.

The brigade not only pursues what the military terms national level targets, such as terrorist kingpin Abu Musab al-Zarqawi, but is also equipped for classic special forces' unconventional warfare and covert operations. Donning civilian clothes, its men dissolve into the streets to scout targets and eye off insurgent mortar sites. U.S. commanders say that during the stand-off with renegade cleric Moqtada al-Sadr's militia in Najaf last summer, their Iraqi charges were "the only Coalition unit to provide daily intelligence from within the Imam Ali mosque". Posing as locals coming to pray, soldiers slipped past Sadr's forces to scope for the militants' command positions, documents and arsenals. It's a skill, and a daring, they learned from the Green Berets. In some operations American Special Forces have worn the flowing Arab dishdasha, with body armor hidden underneath. According to a 1st Cavalry Division commander, a covert team of U.S. troops has used similar tactics to penetrate target houses.

Though the U.S. is pleased with the performance of the commandos, there are also gnawing fears that sending Iraqi units to take on insurgents could fuel sectarian tensions. The vast majority of the ISOF troops are Iraqi Shia, with some ethnic Sunni Arabs; the brigade's deadly snipers are drawn from the core of Kurdish peshmerga soldiers who bolster, and in some cases, command the Special Forces units. It's not the demographic mix the Americans would like, but recruiting from within the Sunni community, which provides the backbone of the rebels' forces, is proving tough.

The Green Berets are watchful of factions emerging within the units. "We keep an eye out for nepotism," says the Task Force Pioneer commander. As a demonstration he turned to the Americans around him, pointing out each man's ethnic origins. "Look at us," he told the Iraqi recruits, "this guy is Polish, he's Mexican, and this guy, I don't know where the hell he's from but he's going to do what he's told." The first 72 hours of training are geared to tackling the cultural divisions with exercises like taking orders from female medics. "By American standards it's not that severe," says an advisor. About 15% of the trainees wash out, he says, compared to half of American recruits failing Ranger School.

So far, the ISOF Brigade is weathering the test. One commando, a 27-year-old former lieutenant from Saddam's army says he joined because he's military through and through, and wanted to continue serving his country. Plus, he adds, his $520 monthly salary is an improvement on the $60 he earned in the defunct Iraqi Civil Defense Corps. Unlike most members of the CTF, he has told his family he was working with the Americans. He's already received two "threat letters" from the insurgents to quit or face death for himself or his family. Still, his family and his new fiancé support him. "They told me, God will protect you and your guys," he says.

Given the desire of the incoming Iraqi government to assume greater authority over the country's security forces, U.S. officials worry that the commando-training program may be curtailed. It's hoped the ISOF Brigade will not be disturbed. There's a long way to go, but these elite troops are the best Iraq currently has to offer. The American Task Force Pioneer commander hopes by building these Special Forces, he is on the way to "working ourselves out of a job" in Iraq. That's a goal both Iraqis and Americans can agree on.

• CHRISTOPHER ALLBRITTON
• On patrol and training with Iraq's new Counter Terrorism force