FALLUJAH, IRAQ--In an old soap factory in the industrial part of town, nearly a dozen U.S. Marine advisers have been preparing the 3rd Battalion of the 1st Iraqi Army Division for its new posting here. The team has been together for more than five months and for all but two weeks has been in Ramadi, withstanding sniper attacks, firefights, and insurgent ambushes. Early on, the big challenges for the marines involved encouraging their Iraqi counterparts to embrace some basic fighting do's and don'ts: "We figured if you don't run, you don't shoot your buddy, and you don't create a blossom of death by firing back at everything that moves, you're doing all right," says Maj. David Richardson, the Marine officer advising the Iraqi battalion commander.

But the potshots of snipers seem straightforward compared with what the battalion now faces, says Richardson, who heads up one of 200 military transition teams throughout Iraq--teams that Lt. Gen. Peter Chiarelli, the No. 2 U.S. commander in Iraq, calls "key and essential" to rebuilding the nation. Today, the team's Iraqi battalion is grappling with critical supply shortages, lack of maintenance know-how, and what one senior military official calls an "unsustainable" attrition rate among Iraqi soldiers.

These challenges come amid efforts to battle an insurgency that keeps creeping back into town--a majority Sunni town that views the battalion's predominantly Shiite Army with suspicion, particularly since a massive offensive by U.S. forces in late 2004 resulted in some of the most brutal street fighting of the war, leaving parts of the city in ruins. Residents who have returned after fleeing the fighting are now required to carry local ID cards in order to pass through the seven checkpoints that surround the city, part of continuing efforts to keep out insurgents.

One recent evening, Richardson and his team meet with Iraqi soldiers, or jundi, for their daily advisory session. Most days, the bulk of their time is spent discussing the shortages the jundi face. "The water, we don't have anymore," says the Iraqi battalion logistics officer. "The ammunition, they don't give us anymore." The Ministry of Defense refuses to increase the water supply, he adds, which it has capped at three bottles per Iraqi soldier per day. It's an untenable limitation, says the battalion commander, considering the battalion conducts three to four foot patrols a day, which often last hours at a time. The battalion also needs electric generators, but there are none to be found in the city.

Like several teams being mentored by military advisers in the area, the 3rd is facing a fuel cutoff next month as well. This "may push some of these battalions to the brink of failure," says the senior military official. American forces, he says, will continue to provide fuel as a backstop, though that's a fact they won't be advertising among their Iraqi counterparts. "It's easy to be the nice guy," says another military official, "but we're not doing them any favors."

Got wasta? Currently, though, it is an army that runs on favors. Here at the camp, Richardson and his team have learned more than they ever thought they would about the concept of wasta, an Arabic term for power and influence through position and contacts, which remains a strong and frustrating fact of life in Iraq, says Capt. Leo Gregory, 30, the advisory team's executive officer. "It permeates everything here." Wasta is a "good-old-boys system," adds Richardson. "But more than that," he adds, "it's a rip-off system." Around the battalion, they say, equipment like coolers has disappeared--becoming gifts, some of the marines speculate, to family members from soldiers on their way home.