Remember Fallujah? For the Barack Obama administratÏion, the Iraqi retaking of Ramadi — with substantial U.S. help — is a welcome New Year’s gift. But before anyone gets too excited about moving on to Mosul, Iraq’s second-largest city, it would be wise to remember that at least two further obstacles remain before that battle can be mounted. The Iraqis need to hold Ramadi and establish supply lines in the territory leading to Mosul, and they must break the Islamic State (IS) group’s hold on Fallujah, to the rear of Ramadi and perilously close to Baghdad.

The first of these goals will be challenging, and for a very specific reason: IS prefers to control territory, but as Iraq retakes that territory, it forces IS to act as an insurgency. And as the long Sunni insurgency of 2003-2006 should remind you, the Sunni areas of Iraq — where the battle with IS is now taking place — are uniquely susceptible to being harassed by insurgent forces.

For example, consider Baiji, a key objective on the main road from Ramadi to Mosul. After nearly two years of fighting, Iraqi forces seem to control it. But several times, IS forces have retaken parts of the city or the oil refinery there despite the Iraqi government’s claim to be fully in charge. Surrounded by barren land, Baiji is vulnerable to hit-and-run-style attacks of the kind favored by insurgents. Kicking IS out of Baiji hasn’t fully guaranteed Iraqi government control.

The Baiji phenomenon can be repeated all along the Ramadi-Mosul route. What’s more, right now, IS’ supply lines honeycomb the sparsely settled desert area stretching from the Syrian border to Mosul. IS in Mosul has large numbers of troops, unlike in Ramadi, where a much smaller number of its fighters had held the town. Beating them requires cutting off those supply lines, a task that requires considerable manpower on the Iraqi side.

To cut off Mosul from IS’ Syrian supply lines, the best force would be made up of Sunni tribesmen who are indigenous to the area and can rely on their own intelligence networks. The government of Haider al-Abadi is trying in a serious way to win over those tribes.

Some Sunni tribes participated in the fight for Ramadi on the Iraqi government’s side, an important sign of progress. A military spokesman said that the security of Ramadi would be handed over to the police and “the sons of the tribes,” evidence that there was a quid pro quo in play. So eager is the Baghdad government to make progress against IS that it’s willing for the moment to give substantial — or maybe total — control over reconquered territory to the tribes.

Yet the tribes remember the insurgency, too. In particular, they know they and other Sunnis were used by Baghdad to defeat al-Qaida and the insurgents — and then promises of self-government were abandoned. Abadi will need to convince Sunnis that unlike his predecessor, he’ll keep his word. That’s a tall order in the distrustful environment of Iraqi denominational politics.

And then there’s Fallujah, the radically anti-government stronghold an hour’s drive from Baghdad that remains under IS control. In 2004, during the Sunni insurgency, U.S. Marines twice fought brutal, house-to-house combat to retake the city from as many as 5,000 al-Qaida-affiliated insurgents.

The “twice” matters. After the initial U.S. victory following the killing of four Blackwater contractors, the marines withdrew, leaving security to Iraqi forces — which soon dissolved, leaving their weapons to the insurgents, who returned. The marines had to do it all over again, at substantial human cost.

Luckily for the United States, at least in retrospect, al-Qaida in Mesopotamia at the time had massed its forces in Fallujah for the battle — which meant that vast numbers of them could be killed. This reflected al-Qaida’s fanaticism, to be sure, but also its lack of a well-defined strategic goal.

So far, IS hasn’t made the mistake of massing forces for sure destruction anywhere. As if it learned the lessons of the second battle of Fallujah, IS’ tacticians have allowed its troops to melt away and fight again elsewhere. For all the IS chatter about an epochal battle at Raqqa, so far that remains an apocalyptic fantasy, not a model to be followed in advance.

It will be interesting to see how IS handles Fallujah this time. The Iraqis won’t come with a force as overwhelming as the marines, because they don’t have one. IS might rationally decide to fight it out there, in the hopes of delaying the attack on Mosul.

But it’s equally likely that IS will eventually fall back from Fallujah, to concentrate on Mosul. States, unlike ordinary terrorists, can afford to lose territory to prioritize for future efforts to hold other territory. And IS badly wants to be a state.

The Iraqi government’s fight with IS is just getting started. And perhaps the most sobering post-New Year’s realization must be that if Iraq wins, IS doesn’t necessarily lose. It can just redouble its efforts in Syria.

Noah Feldman, a Bloomberg View columnist, is a law professor at Harvard University.

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