Al Qaeda remains the biggest threat, and over time Coalition and Iraqi forces have killed, captured or run off substantial numbers of the terror group. But there is still a lot of work to do in the Diyala and Tigris river valleys, and in Iraq's second-largest city of Mosul and surrounding Ninevah province.
"We are going after al Qaeda relentlessly wherever they are, and wherever we can find them, we put our teeth into their jugular," Petraeus said.
Mosul is an important place to al Qaeda. "Analysts have said that while Baghdad is critical for al Qaeda to win in Iraq, Mosul and its area is critical for their survival," the general said. Recent successes notwithstanding, Petraeus warned, a "final battle" with the terrorist group is not imminent.
"Al Qaeda is incredibly resilient," he said, "and they are receiving people and supplies through Syria - although numbers through Syria are down as much as 50 percent."
Coalition and Iraqi forces will take on al Qaeda in the north, but will do so on their timetable and according to their plans, the general said. He will not start shifting U.S. and Iraqi forces willy-nilly around the country.
"The key is to hang on to what you've got," he said. "You cannot, in your eagerness to go after something new, start to play ‘Whack-a-mole' again. You have to hang onto the areas you've cleared; you have to have that plan to do before you go."
Coalition forces are moving to Mosul and Ninevah, but Petraeus said he will not risk losing gains made in Baghdad, the belts around Baghdad and in Anbar province to do so.
"Al Qaeda is trying to come back in," he said. "We can feel it and see it, and what we're trying to do is rip out any roots before they can get deeply into the ground."
The bottom line militarily in Iraq is a "feel" for the country and the determination of what constitutes an acceptable risk, the general told reporters. "At the end of the day, it's about feel," he said. "We have commanders in most cases on their second tours in Iraq, some on their third. Over time, you can start to feel where you can take a bit more risk and also where you cannot.
"You have to walk the streets, talk to the leaders, talk to your own commanders and then you bat it around every day," he said.
Petraeus said he doesn't feel any anxiety over his decisions.
"If you want to talk about anxiety, talk about coming back to Iraq in February 2007 and being greeted by 42 car bombs," he said. "The level of attacks was more than 150 a day, and our losses were exceedingly tough."
With so much chaos in the country, it was hard just trying to get a handle on where forces needed to go, the general recalled. "We've worked our way through that," Petraeus said. "These additional concerns are very serious, but we're working on those with the Iraqi government."