Although U.S. troops have punched into the center of the Iraqi city of Fallujah, they might later encounter many more insurgents who have escaped, perhaps to fight another day in another place.
"I personally believe that some of the senior leaders probably have fled," said Army Lt. Gen. Thomas Metz, the multinational ground force commander in Iraq.
Senior military leaders also said today that despite the fierce battles in the city, the fight will be over in a matter of days.
"They [insurgents] seem to be fighting in very small groups, without much coherence to the defense after that initial attack we made," Metz said.
According to Metz, Iraqi insurgents have suffered significant losses, greater than the U.S. military anticipated. He also said there have been very few civilian casualties.
"We felt going in that at least half, if not 75 percent, of citizens had left Fallujah," Metz said. "We have seen very, very few civilians on the streets in Fallujah."
Part of the reason the battle could end soon is that many of the insurgents may have left the city before it even began, including, said Metz, the men in charge.
Commanders are also concerned about what one senior military officer described as the "Fallujah effect," with insurgents throughout the country launching attacks in support of those who remain in the city.
In Ramadi, hundreds of armed militants flooded the streets, as U.S. helicopters kept watch over head. In Baquba, an Iraq police station was ambushed, killing one officer and wounding eight others.
In Baghdad, car bombs hit an Iraqi police checkpoint at a hospital, as well as two churches. Further north in Kirkuk, another car bomb exploded, and two U.S. soldiers were killed in mortar attacks in Mosul.
The continued violence means that even if the battle of Fallujah is successful, the problems will not be over.
"We don't know how many people can go underground, simply go back into the population, or how many can escape what is a loose surrounding force around the city," said military analyst Tony Cordesman, an ABC News consultant. "We have to understand this is a battle. It is not a war."
There are still concerns that the insurgents are regrouping inside Fallujah for a final assault.
ABC News' Martha Raddatz filed this report for World News Tonight.