But also because the Iraqis have been learning on the job; in ferocious battles in Tikrit and Baiji earlier this year, where they also managed to push ISIS out.
Britain on Monday congratulated Iraq after the city of Ramadi was recaptured from the Islamic State jihadist group.
Mosul, northern Iraq's main city, is by far the largest population centre in the self-proclaimed caliphate ISIL rules in Iraq and Syria after going on the offensive in June 2014.
Iraqi forces, though backed by U.S.-led coalition air strikes, had been slowed in Ramadi by explosives planted in streets and booby-trapped buildings by Islamic State fighters. In the face of that, Alice notes, ISIS is trying to emphasize its control - and to tap into grievances in Yemen and elsewhere to help it establish franchise groups. He said at its peak there were up to 1,000 IS fighters in Ramadi, and that only 150-250 remain.
The battle for Ramadi was waged by the Iraqi military - rather than Shiite or Kurdish militias - with elite counterterrorism units advancing under the cover of coalition airstrikes and raising the Iraqi national flag over the main government complex in the provincial capital on Monday.
"To use the same approach everywhere in the region... the scale of damage would be huge", she said.
USA officials appear to be more cautious about the scale of the challenge than their jubilant Iraqi counterparts.
By Dec. 22, much of the eastern half of the city had been retaken by Iraqi forces.
"The fight for Falluja is ongoing".
"Essentially, they encircle the city, nearly like a boa constrictor, and they will then squeeze in closer and closer into that city until eventually they are able to finally clear it, as we saw in Ramadi", Warren told reporters. And it may prove to be a rallying point for jihadists once again.
"There are other military sources that say this might be a bit unrealistic", Alice says, "based on the fact that Fallujah and Mosul are heavily populated", unlike Ramadi and other ISIS-controlled cities that have been retaken.
"There were no Shia militias involved in this operation for Ramadi", Warren said.
Ramadi is a city in the Anbar province, which is about 110 kilometers away from Baghdad.
Pockets of resistance remain, but the majority of Ramadi is under government control for the first time since May, when IS militants punched their way into the city with a series of massive suicide vehicle bombs, scattering and humiliating Iraq's beleaguered security forces.
The city, which tens of thousands of people fled during months of fighting, will need to restore basic infrastructure like electricity and running water, as well as its residents' sense of security.