After nearly a month of intense fighting, Islamic State fighters appear to have retreated from some of their main fighting positions in Fallujah. Reports from earlier today say the Iraqi forces have advanced to the center of the city, retaking a large hospital, several central neighborhoods and the main government compound. While this is a symbolic victory against IS, our model tells us that its overall importance will be somewhat muted.

Though the Islamic State has occupied the city since the end of 2013, its fighters have retreated, with some regrouping to Fallujah’s western neighborhoods and others heading further west into areas more firmly controlled by IS. According to a U.S. spokesperson, approximately a quarter of the city is under the control of U.S.-backed coalition forces, and after a difficult start to the Fallujah operation, there is optimism on the ground that Iraqi forces will be able to make continued progress in taking the rest of the city.

The Iraqi commander of the offensive told the Guardian that the Islamic State’s leadership in the city is gone and that the majority of its fighters have fled towards the west. Iraqi officials have boasted about their success before, so it is important to take their claims with a grain of salt, especially considering that a few weeks ago IS managed to halt the Iraqi army’s advance into the city. Parts of the city remain under IS control, and IS has had ample time to prepare defense and booby traps. IS will likely retreat from Fallujah in the end but not before exacting more casualties on coalition forces and on the civilian population.

Retaking Fallujah is a symbolic victory for the Iraqi government, but in terms of actually crippling IS’ ability to continue operating in its core territories and to undertake attacks on Baghdad and other Iraqi cities, it means relatively little.

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Fallujah is 40 miles west of Baghdad, and because it was one of the first cities IS held, it is an important symbol for the group, but holding Fallujah from a tactical perspective is not crucial to IS defending its main holdings in Syria and Iraq. As we have laid out in a Deep Dive study of the Islamic State, there are four potential approaches towards meaningfully attacking IS core territory. Winning back Fallujah from IS does not advance any of those imperatives, nor does it portend an immediate shift to a massive assault on Mosul.

We do not mean to minimize the loss of Fallujah for IS. It is certainly a city IS would prefer to hold on to. But even once Iraqi forces are able to control the entire city, its loss will not be a decisive one. In addition, since 2003, Fallujah has repeatedly fallen under control of jihadists. Given the underlying sectarian divides, which will not to be solved any time soon, it is very likely the city could once again fall into jihadist hands. Retaking the city was the easy part – administering it will be much more difficult.

There is also the question of whether the majority Sunni population in Fallujah and the surrounding area will be comfortable with the presence of Iranian-backed Shiite militias that are part of the forces Iraq has relied on to take back the city. Already, there have been reports of attacks and execution-style killings by pro-government forces against locals. Fallujah was a fertile breeding ground for IS because locals were distrustful of the government in Baghdad, and taking the remainder of the city will be far easier than addressing the plight of its civilians and gaining their loyalty.

Our model of IS tells us that IS is facing serious pressure from U.S.-backed forces in both Syria and Iraq – but Fallujah was not one of the places we identified as crucial to that battle. The retreat from Fallujah demonstrates the pressure that IS faces in its core territory and its need to pull back to more defensible positions. Taking back Fallujah makes those positions no less defensible – and if Iraqi forces entering the city leads to an increase in sectarian tensions, Iraqi control over what is left of the city may be tenuous at best.