"They come up in their Opels, attack and leave," says a business owner in the heart of Mosul, explaining how insurgents operate in Iraq's northern capital.
Intelligence gathering is the best way to catch them, US military officials say, while some security experts say killing their leaders may be the only way to defeat them.
But the rebels have proven that they are masters of their terrain and are feared by ordinary citizens.
"We are going to set up a permanent secret service outpost here," promises Major General Rashid Flaih, head of a 500-strong commando force recently sent from Baghdad to help a US-led effort restore order in the city.
His men have rounded up at least 52 suspects over the past week for interrogation, capturing them in raids on the old quarters and on a hospital where they thought wounded insurgents were being treated.
Flaih says that most of the insurgent activity in Mosul is fueled by a few hundred men who flock into the city from surrounding villages and some foreigners, predominantly Syrian, who come over the nearby border.
They settle with their kinsmen in troublespots like Al-Yarmuk, Al-Islah and Al-Tanak on the west side of the city, taking advantage of tribal and family ties.
"I cannot say Mosul has been cleansed. There are pockets which we will break after we have gathered a very strong base of intelligence," says Flaih.
US security officials say they are pinning their hopes on the recently created commando force to move quickly into trouble spots all over the country and target insurgents with precise intelligence.
"The key is for units to go out there and target their leadership; there are some of these guys that have to be killed," says Jim Steele, an advisor to the commando force.
"You have to disorganize them. You have to employ some of their same tactics: you are on the offensive and you are ambushing them."
Steele predicted that insurgents in Mosul and across Iraq have grown more desperate as they see the clock ticking towards national elections at the end of January, and that they will launch bolder and bigger attacks.
He concedes that rebels have gained a tremendous time advantage to organize themselves and perfect the art of hit-and-run operations, because until recently Iraqi forces were weak and the US-led coalition was the only sheriff in town.
"If the coalition has to do it, it has a feeding effect on the insurgency," says Steele, referring to the level of sympathy among the general population towards the insurgents.
But if events in Mosul over the past two weeks are any indication for the rest of Iraq, US-led forces look like they still have to play the role of the tough cop for some time given the problems plaguing the country's fledgling security forces.