Pentagon officials hailed the U.S.-trained Iraqi army this week for retaking much of the western Iraq city of Ramadi from the self-proclaimed Islamic State.

But privately, Defense Department officials tell The Daily Beast the fight for Ramadi was a long slog led not by the army, known as the Iraqi Security Forces (ISF), but by an elite counterterrorism force, which itself was only able to beat ISIS with U.S.-led coalition airstrikes. The ISF, which have been the beneficiaries of years of U.S. training and funding, didn’t lead the battle, but served in a support role, pointing out ISIS positions for air attacks and holding the roads that led to the city center where troops Monday flew the Iraqi flag.

It’s one of several ways in which the simplistic narrative of the battle for Ramadi is giving way to a more nuanced story—one that presents both promise and peril as the fight against ISIS continues. For those looking for good news, there was plenty: the emergence of Iraq’s elite fighters, and the apparent absence of the Shia militias which have threatened to turn the ISIS conflict into a sectarian war.

But there was troubling news as well. The Iraqi army’s inability to lead the five-month battle for Ramadi leaves many in the Pentagon dubious of plans to liberate ISIS’s biggest Iraqi stronghold, in Mosul, despite pronouncements from Iraqi political leaders that the operation is on the horizon. The ISF can, at best, carry out the ancillary aspects of war fighting. And the elite counterterrorism unit is not large enough to do the job of liberating—and holding—multiple cities simultaneously.

The battle of Ramadi suggests that Iraq’s counterterrorism forces, an elite group akin to the U.S. Army’s Special Forces, are the Baghdad government’s most capable fighters. They can move block by block with the backing of coalition air forces that kill scores of ISIS militants, so that Iraq’s conventional forces don’t have to confront them.

“This was attrition warfare. This was not an aggressive ISF ground campaign. They were mostly coordinating and providing security for the counter terrorism unit and maintaining a perimeter, which can be quite taxing,” one defense adviser to the war on ISIS explained to The Daily Beast. “It was mostly about pinpointing ISIS positions to call in airstrikes, clearing booby traps so you could open up mobility corridors.”

It’s one of the many ways in which Iraq’s forces—especially its conventional forces—are limited. The ISF cannot clear cities filled with civilians, hold multiple cities, or win territory without punishing coalition airstrikes that leave places like Ramadi demolished, two defense officials told The Daily Beast. Mosul, Iraq’s second-biggest city, whose fall in June 2014 led to the latest American intervention, is still heavily populated with civilians.

And even in victory, roughly 30 percent of Ramadi remains under ISIS control, the officials said.

The Iraqi Security Forces “aren’t doing house cleaning. I don’t think they have the depth, experience, or numbers to be able to consistently conduct clearance operations in contested, urban areas,” said Christopher Harmer, a naval analyst at the Washington-based Institute for the Study of War. “It appears that they are approaching the fight, and when it exceeds their capabilities calling in American airstrikes. It takes a long time and there are severe limitations with that kind of warfare.”

The early figures provided by the Pentagon also suggest that conventional Iraqi forces were not engaged in prolonged fighting. Operation Inherent Resolve spokesman Army Col. Steven Warren told reporters Tuesday that the Iraqi Security Forces took less than 50 casualties; that there was no indication of ISIS fighters being captured; and that the airstrikes were 80 percent of the reason the city fell.

The U.S.-led coalition has conducted 630 airstrikes in Ramadi since the battle for the city began in July, 150 of them in the last week alone. Defense officials said most of the roughly 1,000 ISIS fighters entrenched in Ramadi were killed in airstrikes; the remaining fled northeast of the city.

The U.S. military still doesn’t know how many civilians have been killed. Warren said roughly 400 civilians fled to the city government center once Iraqi troops moved in, on the backs of their elite force and coalition air power. At its peak, Ramadi had nearly 200,000 residents. Images from the fallen parts of the city showed an area all but destroyed.

Publicly, the Pentagon defended the Iraqi military’s prowess. Warren called the troops in the battle of Ramadi as “tough as any other fighter out there.” The retaking of Ramadi marked the biggest victory for the Iraqi forces, in a city that ISIS held for the least amount of time, seven months. ISIS also has lost control of the Iraqi cities of Tikrit and Sinjar in the past year.

But while many suggested that Iraqi Security Forces could tackle ISIS’s hold on places like the nearby city of Fallujah or even Mosul next, the U.S. military wanted to first see how the Iraqis held Ramadi—and whether it would remain a majority Sunni city while under the control of the Shiite-dominated government and military.

“The hard part of Ramadi is still to come,” the defense adviser explained. “This is the easy to stuff. How are you going to hold it if you have not addressed the political, economic, and humanitarian issues? How are you going to hold it if you don’t have the military structure that is reliable? You can’t hold Ramadi, and Tikrit, and the area the around the Tigris River valley and take Mosul. If you don’t see humanitarian support [the battle of Ramadi] would just have been ethnic cleansing” of Iraq’s Sunni population.

A documentary released online by Vice last week purports to show soldiers from the battle-hardened and elite Golden Division—one of the few non-sectarian units in the Iraqi military, made up of Sunnis, Shiites, and Christians—fighting in Ramadi. (The claims could not be confirmed by the U.S. military.) One Golden Division soldier, Ahmed, himself a Shiite, had been kidnapped, tortured, shot, and left for dead by a Shiite militia. Other members of the unit told Vice that while the Golden Division could retake Ramadi, only Sunnis in the Iraqi military could ultimately hold the city.

Ramadi fell into ISIS hands shortly after Iraqi forces reclaimed the nearby city of Tikrit. Early on, Secretary of Defense Ash Carter suggested the ISF did not have the “will to fight” for Ramadi.

The battle for Ramadi suggests the will to fight has grown, but not necessarily for the kind of combat needed to keep ISIS out of multiple Iraqi cities.

In an effort designed to avoid sectarian tension, Iraqi Prime Minister Haider al-Abadi ordered that Shiite militias, which are backed by Iran, would not participate in the Ramadi operation, U.S. officials and sources in Iraq who are knowledgeable of the decision told The Daily Beast.

The militias appear to have heeded that order: U.S. officials said that the various units, which fall under the umbrella of the so-called Popular Mobilization Forces, didn’t participate in the operation to recapture the city. The officials added that while there were some Iranian-backed militia fighters in the area, donning Iraqi Ministry of Interior uniforms, they did not have a major role in the battle.

That’s a big deal. Those forces have played a decisive role in previous battles against ISIS. So the decision to exclude them wasn’t without risk.

But the Shiite fighters were also accused of sectarian violence after those earlier battles were won—and were painted as pawns of the Iranian regime.

Keeping those militias out of the Ramadi operation was a way of blunting the idea that the combat was merely a power play by Iran. It also gave the Iraqi army the chance to rebuild its confidence and use the training that has been provided by the U.S. and its coalition partners, one U.S. official said. The central government plans to hand over security in Ramadi to local, Sunni forces, so avoiding any sectarian conflict bolstered that plan and avoided a repeat of the violence seen during the liberation of Tikrit, last spring, when Shiite militias were accused of vandalism and looting against local Sunnis, including those whom they believed were supporting ISIS.

The extent to which U.S. officials were involved in the decision to exclude the militias was disputed.

“The U.S. government took no position on the prime minister’s decision not to include the [Popular Mobilization Forces] in the Ramadi operation. We did not encourage it, nor have we questioned it. We played no role,” State Department spokesman John Kirby told The Daily Beast.

But keeping the Shiite militias out of Ramadi was part of discussions among U.S. military and diplomatic officials, Iraq’s prime minister, and fighters from various Sunni tribes who took part in the operation, Mark Alsalih, a Sunni lobbyist in Washington and the president of the Iraq Stability and Security Program, composed of citizens and tribal sheikhs, told The Daily Beast.

“The tribal fighters had a pre-condition going into this,” Alsalih said. “If you want us to jump in with selected units of the Iraqi army… we don’t want any of these Popular Mobilization Forces around us.” Those Sunni fighters were essential to the mission’s success, Alsalih said, because they knew Ramadi neighborhood-by-neighborhood. Some of them were from the city and had left after it was seized by ISIS.

The exclusion of the militia forces—which are estimated to number as high as 120,000 men, more than twice the size of the Iraqi army—has raised questions about whether Abadi is trying to diminish their influence, and by extension, Iran’s. The militias are largely a creation of Abadi’s predecessor, Nouri al-Maliki, whose continued influence in Iraqi politics Abadi is said to fear.

The more than 40 different militia groups aren’t under the control of Iraq’s military, and their loyalty to the government in Baghdad varies, experts say.

Alsalih said that Abadi’s decision to exclude the militias, also known as the Hashd al-Shaabi, had led to a dust-up between him and Abu Mahdi al-Muhandis, an Iraqi military commander who’s in charge of coordinating the fighters’ activities. Muhandis is no friend of Washington: He was sanctioned in 2009 by the U.S. Treasury Department, which said he was an adviser to the notorious Iranian general, Qassem Soleimani, and was responsible for attacks against the U.S. and ISF. Muhandis was also convicted in absentia for his role in bombings at the U.S. and French embassies in Kuwait in 1983.

Iraqi news outlets carried accounts that Muhandis had been removed from his post, a claim that couldn’t be verified and that one Baghdad-based political analyst disputed.

“Muhandis was complaining of U.S. involvement and their demands for no Hashd involvement rather than the prime minister’s orders,” the analyst, who asked not to be identified by name, told The Daily Beast. “Muhandis is still in his post. The prime minister has not fired him.”

Any break between Abadi and the militias would be significant, because it could mean Iran’s influence over Baghdad via its own proxy forces in Iraq is waning, or that Abadi aims to challenge it.

The analyst, however, said that the Hashd was generally willing to stay out of the fight in Ramadi because it “didn’t really have the manpower to be involved anyway.”

“The Hashd is not a monolithic organization. In fact it is essentially a group of 45 competing forces that differ in their allegiances and their backing, and the prime minister is closer to some groups than others,” the analyst said.

The absence of an Iranian-backed force in the fight for Ramadi was arguably a significant strategic victory for the U.S.-led coalition to oust ISIS, which would prefer to diminish Iran’s influence and its alliance with Russia. But others cautioned not to assume that just because the Shiite forces weren’t on the ground this time they won’t return.

There are militias stationed just to the east of the city, at the Habbaniyah military base, Patrick Martin, a researcher who focuses on political and security issues in Iraq at the Institute for the Study of War, told The Daily Beast.

“As forces shift, we should expect ISIS to test the capabilities of these new Sunni security forces,” Martin added of the groups that Baghdad aims to put in Ramadi.

And if ISIS were to return to Ramadi, there’s no guarantee the Shiite militias would stand down again.