"You say Fallujah is a real success story. What turned it around?" asked CBS Evening News anchor and managing editor Katie Couric.
"What turned it around was the local population deciding to reject al Qaeda," said Petraeus.
After U.S. troops retook the city by force in late 2004, life is now slowly returning to normal. Fallujah is safer. The relationship between American troops and Sunnis is strong.
How important was the surge in getting this done?
"It gave us an ability to clear and to hold some areas that were sanctuaries for al Qaeda in the past," Petraeus said. "And then what happened is you have a situation where you are spiraling upwards instead of spiraling downwards.
The powerful tribal leaders of Anbar province, who are really the heads of large extended families, rejected the harsh, brutal tactics of al Qaeda. Sheik Saddoun Al Bou'issa lost 30 members of his tribe.
"We think they care about Islam, but they lie, they cut heads, they destroy Iraq. They don't like Iraq to be safe," Saddoun said.
Now his greatest worry is that al Qaeda will return if the Americans leave.
"We ask the Americans to help us until we finish al Qaeda. If they back one step, they will destroy everything we build," he said.
The decision by the tribal leaders to fight al Qaeda spread across Anbar province, and it made joining the Iraqi security forces an honorable choice. The Iraqi police force grew by more than 200 percent in just the last year, to 19,000. Violent incidents have dropped from more than 1,400 last March to just over 400 in August.
While these new recruits rely heavily on U.S. training and equipment, they want them here now, but not indefinitely.
When asked if they would rather have U.S. troops here than al Qaeda, a recruit told Couric: "A time will come when al Qaeda is gone, and a time will come when the Americans will go as well."