Ask Bush administration officials to explain America's strategy in Iraq and they offer what amounts to a two-word answer: "Ayad Allawi," the interim prime minister who is in the United States this week for a round of meetings and media visits.

"It's great to have an Iraqi prime minister taking the lead instead of an American occupation authority," says Paul Wolfowitz, the deputy secretary of defense and one of the architects of the war. The issue now in Iraq, he says, is, "Can Allawi win it?" That view is shared by other top administration officials, who use words such as "indispensable" when they describe Allawi's role.

But this reliance on Allawi as a "strongman" in Baghdad raises the question: What is the real U.S.-Iraqi plan for regaining control of the country, and is it likely to succeed? At a time when much of the news from Iraq is dismal, how realistic are Allawi's hopes for pacifying his nation in time for January's planned elections?

A rough outline of the Bush-Allawi strategy emerged in recent conversations with U.S. officials in Washington and Baghdad. It's an approach that hinges on many unknown factors. Given the stakes, it's important that Iraqis and Americans understand those risks.

Allawi's primary assumption is that as a Shiite Muslim, he can retain the support of Iraq's majority Shiite population. He views the insurgency led by radical Shiite mullah Moqtada Sadr as a tactical problem that is gradually being solved. In this he counts on the backing of Shiite Grand Ayatollah Ali Sistani.

Last month's battle against Sadr's militia in the holy city of Najaf provided the clearest evidence of Allawi's approach. The fight there began by accident in early August when U.S. Marines raided a house in Najaf without realizing that Sadr was hiding out two blocks away. Sadr quickly launched a well-planned insurgency of his own.

Allawi decided on an aggressive counterattack by U.S. and Iraqi forces. The Americans sent every available sniper to Najaf, and over the next weeks, they killed more than 1,000 of Sadr's militiamen. Sadr and his followers retreated to the Imam Ali mosque, hoping that Allawi would balk at an assault there. But the Iraqi leader decided to storm the mosque -- using brave but untested Iraqi security forces.

Top U.S. officials weren't convinced that storming the mosque made sense, but they backed Allawi anyway. U.S. commanders hoped the Iraqis were ready, but to senior administration officials back in Washington, it seemed like placing a large bet on an uncertain outcome. President Bush himself is said to have deferred to Allawi's judgment, arguing, "He's a Shiite. It's his country."

Just as the Iraqi forces were gathering for the decisive assault on the shrine, Sistani decided to return from a medical visit to London. Allawi initially hoped to delay his return, but when he came anyway, Allawi sent emissaries to work out a negotiating strategy to remove Sadr's militia from Najaf. In the end, Sistani's mediation succeeded, and both Allawi and his U.S. advisers count it as a victory.

"The result in Najaf is as good as if it has been done by force," Wolfowitz says. "The downside of storming the mosque was that things could have gone disastrously wrong."

The Sunni insurgency centered in Fallujah remains the real strategic challenge for Allawi. His approach is to combine punishing U.S. air attacks with political appeals to mainstream Sunni leaders in an attempt to isolate and eventually destroy the insurgents. In meetings with Fallujah leaders, Allawi has warned that a bloody assault is coming if they continue harboring the resistance. His message, in effect, is, "Expel the insurgents or we'll blow down your city."

U.S. officials are reassured by Iraqi demographics. They reckon that the Sunni insurgency can never grow larger than the Sunnis' 20 to 25 percent share of the Iraqi population. Iraqi Shiites and Kurds will never support the Sunni rebels, they believe.

Allawi knows he will eventually have to surround Fallujah and regain control by force. As in Najaf, his model seems to be combined U.S.-Iraqi military operations -- led by Iraqi forces. Those forces will include a mechanized brigade, which Washington recently approved over the objections of some U.S. commanders. The military showdown in Fallujah will take place "no later than the end of this year," says a top official.

Can Allawi win it? That is indeed the question, and U.S. officials can only hope the answer is yes -- and accelerate the training of Iraqi forces. If Allawi fails, there doesn't appear to be a Plan B.