As the red, white and black flag of the Iraqi government was raised over the government compound in Ramadi, Iraq, on Monday, leaders of the U.S.-led military coalition against the Islamic State faced a new question: How do they and the Iraqi military recapture that success in other cities, some of which could be even tougher to win?

Ramadi, a city of about 220,000 people, fell to the Islamic State in May 2015, after months of the militants attacking Iraqi security forces, and eventually overwhelming them and prompting survivors to flee. Iraqi military efforts to take back the city began a few months later, but it wasn’t until the last few weeks that it seemed like possession of the city, the capital of Anbar province, was poised to change.

Army Col. Steve Warren, the top spokesman for the U.S.-led military coalition, told reporters at the Pentagon on Tuesday from his headquarters in Baghdad that Ramadi still is not 100 percent cleared, and could be home to guerrilla warfare in the future as remaining militants attack Iraqi police and soldiers with improvised explosive devices, small arms and rocket-propelled grenades. But he said that it does not appear that the Islamic State has the combat power to take back the government center.

“We have not seen this enemy able to mass any type of combat, any type of real combat power in any type of effort to really conduct a conservative counterattack,” Warren said. “It doesn’t mean it’s impossible, it just means we haven’t seen it yet. We believe the majority of this enemy has been dispersed into smaller pockets. Many have moved kind of north and east.”

On the heels of other victories against the Islamic State in the Iraqi cities of Sinjar, Bayji, Tikrit, the victory in Ramadi suggests a blueprint may be emerging on how the Iraqi government and the international military coalition partnered with it can taken control of Mosul, Fallujah and other Iraqi population centers still controlled by militants.

That strategy includes not only overwhelming Islamic State fighters with coalition air power, but gradually choking off their supply routes and boosting the capability of the Iraqi security forces with specific training and equipment they did not previously have. That includes floating bridges used to cross into militant-held neighborhoods over water and devices that counter the deadly network of improvised explosives and booby traps they have laid.

In the months up until Monday’s seizure of the government center, Iraqi forces approached Ramadi systematically, much as U.S. forces had done in similar campaigns in both Iraq and Afghanistan. The initial phases, known as “shaping operations,” involved Iraqi troops seizing and holding routes that led into the city. Following these early operations that managed to somewhat seal off the city, Iraqi troops began to enter into Ramadi itself.

Momentum for the operation initially stalled, however, because of the multitudes of IEDs that had been placed throughout the city. In an effort to counter them, U.S. and coalition advisers surged explosive ordnance disposal equipment and additional training to Iraqi forces.

What resulted from the renewed focus on countering the Islamic State’s IEDs was a hybrid strategy of sorts, including a Mine Clearing Line Charge, or MICLIC, which works by launching a series of explosives on a single line onto a battlefield and detonating, clearing a path for soldiers on foot to cross. A MICLIC allowed the Iraqis to get into the southern part of Ramadi in the last few days.

Additionally, the Iraqis used 21 armored bulldozers in the city to push up dirt berms to provide protection on the flanks of Iraqi troops from suicide attacks. They had trained with them with U.S. forces ahead of time.

“They use them to rapidly built up berms on the sides of an advancing unit,” Warren said of the bulldozers. “Because this enemy likes to try and bring truck bombs — or we call them VBIEDs — around and into the flanks of attacking forces.”

At the peak of the Islamic State’s control over Ramadi, there were up to about 1,000 enemy fighters in the city, Warren estimated. That number plummeted in recent days to between 250 and 350 as Iraqi troops closed in on the city over the weekend. Other fighters likely fled to east of the city in an area along the Euphrates River known as the “Shark’s Fin.” That area — shown in the map below surrounded by green areas now controlled by the Iraqi government — will likely be a focus of the military coalition in coming days.

The fight for Ramadi also highlighted the shifting mission of Iraq’s Counterterrorism Service, or CTS, to serve as a kind of light infantry unit in the assault on the city. Established after the U.S. invasion of Iraq in 2003, it was initially an aggressive raid force, but was needed in a more conventional military role after the Iraqi security forces took heavy losses in their defeat to the Islamic State in Mosul early in 2014, as noted in this report released this year by the Brookings Institution. The CTS also previously served as a backbone in successful operations in Tikrit, Samarra and Baiji.

Warren said Tuesday that the Iraqi military that collapsed against the Islamic State last year was focused on checkpoint operations and counterinsurgency, and not prepared for attacks in which enemy forces massed and then launched coordinated attacks against them. Aside from the CTS, most of them also were not prepared to launch assaults like the one in Ramadi this week, Warren added, underscoring a training need for the Iraqi military in coming weeks and months.

Initial phases of an operation to take back Fallujah and Mosul — which have populations of more than 320,000 and 1 million, respectively — already are underway. The Iraqi military and U.S.-led coalition have not indicated which city will be the primary focus next to keep the element of surprise, but Warren said Tuesday that Fallujah already has been encircled by Iraqi security forces from three sides.

“Many of the same tactics applied in Ramadi are being applied in Fallujah,” Warren said. “We don’t have a timeline yet. As I’ve said before, the enemy does get a vote here, so we’ll have to see how the fight progresses.”

In Ramadi, meanwhile, Sunni tribal fighters are expected to begin operating in the city’s center to provide security. These fighters did not have much of a role in the taking of Ramadi, Warren said, but are expected to provide an option that the Pentagon prefers over relying on the Shiite-dominated Iraqi security forces.

That, too, could be important in other cities, including Fallujah. The Sunnis are the dominant population across Anbar province, and considered far less likely to rebel against the government if the security forces around them understand them and are likely to work with them.

An earlier version of this post incorrectly stated that Ramadi fell to the Islamic State in May 2014, when it was in fact May 2015.