The battle for Fallujah began, after months of unheeded calls for surrender, with a massive air and armored attack by 10,000 troops whose goal was clear: capture or kill the 3,000 insurgents thought to be in the city. Yesterday, Defense Secre-tary Donald H. Rumsfeld was asked by reporters whether the battle would continue until there was a “clear and final” victory, and he replied: “I cannot imagine that it would stop without being completed,” meaning until the insurgents were vanquished.

Overwhelming force, clear goals, understood conclusion: The assault on Fallujah supports at least part of the Powell Doctrine in a way the Iraq war has not seen before. If it is successful, it will vindicate one side of a prolonged debate about the war: Was the Army correct in wanting more troops for the war, especially to hold Iraq once the initial fighting had been completed?

Secretary Rumsfeld’s vision of a quick, relatively small, technologically advanced fighting force gained supporters after its success in Afghan-istan and in the early stages of the war in Iraq. But its shortcomings became apparent after the capture of Baghdad, when the United States pivoted from winning the war to trying to win the peace. Chaos followed, as did an inability to secure national borders, time for the insurgents to regroup and attack. U.S. troops faced an unexpected level of risk more than a year after victory was declared, and Iraqi patience wore down during the long, hard slog. If there has been a policy change in Washington, it will be seen in the number of coalition troops that occupy Fallujah once it has been fully taken.

The Powell Doctrine grew out of the secretary of state’s experience in Vietnam and set as conditions for war that it be a last resort with a national interest at stake, public support, overwhelming force when executed and an understood exit strategy. There is no national interest in Fallujah, though the doctrine doesn’t necessarily apply to each battle of a war. Many of the other conditions exist, however.

Reports from Fallujah yesterday had American forces pushing deeper into the city, through narrow streets and blind alleyways, the sort of fighting the United States had hoped to avoid in the war. So far, fortunately, casualties are reported to be light, though U.S. officials said they expected the insurgents to try to draw troops into the center of the city. Col. Craig Tucker told The New York Times, “They’ll try to pull us into the city. They’ll win if it’s bloody; we’ll win if we minimize civilian casualties.”

The coalition forces will also win if they can stop the infiltration of insurgents from across Iraq’s borders and persuade Iraqis themselves not to join that movement. That will require a renewed major effort, and while Iraqi troops will be essential in this effort, so will Americans. The doctrine being applied in Fallujah may be usefully applied to this, as well.