What’s the next step in the war against Islamic State-based terrorism? U.S. presidential candidates have talked about their plans to “smash the would-be caliphate” (Hillary Clinton); “knock the hell out of ISIS” (Donald Trump); and “carpet bomb them into oblivion” (Ted Cruz). Republicans and Democrats in Congress have made similar statements but have yet to pass new bills to authorize use of military force.

Is military might in Syria the best way to combat the group, also known as ISIS? Our new article, forthcoming in the journal Terrorism and Political Violence,  examines the coalition’s use of violence to suppress insurgency during the Iraq War. We found that excess reliance on military force can produce counterintuitive results.

Using data from the Iraq War Logs, we analyzed the numbers to see whether killing insurgents had any influence on the incidence of insurgent attacks. We constructed a weekly data set across 103 districts in Iraq from 2004 to 2009. The data counted how many insurgents coalition forces killed each week in each district, through all types of military engagement (including direct and indirect fire incidents, bombings or any other form of engagement where a member of the coalition was present to record the incident). We then analyzed whether the number of insurgents killed in a given week had an impact on the number of insurgent attacks against coalition forces in future weeks. The answer is yes — but it turns out that rather than reducing the insugency’s  capabilities, killing fighters actually encouraged more attacks against the coalition.

When coalition forces employed extreme violence — killing relatively large numbers of insurgents — they were able to moderate the rate of increase in insurgent attacks, but not reduce it. In other words, military force alone was not successful at decreasing violence in Iraq. Here are four reasons why.

1) Military force often means collateral damage.

Military strikes of all sorts also kill civilians, damage infrastructure and restrict economic activity. This collateral damage can harden public sentiment against the coalition, and increase civilians’ willingness to join or support militant movements, a phenomenon observed in Syria already.

Even if they choose not to take up arms, civilians who lost a friend or family member to a military strike may begin to harbor attitudes that favor militancy, especially if they view these deaths as unjust. Communities that discuss terrorist attacks openly and where people’s statements about militant activities receive tacit support can create a culture that supports terrorist activity. The result can validate terrorist propaganda, cultivate narratives of heroism surrounding those who join and fight, and increase the movement’s appeal to locals. Indeed, scholars argue that suicide bombing is on the rise due to increasing cultural acceptance of it as a form of martyrdom. The Islamic State’s ongoing capacity to attract followers at home and abroad, despite years of coordinated airstrikes, offers supportive evidence.

2) Civilians are likely to blame outsiders for violence, not the Islamic State.

This anti-coalition sentiment can persist even when militants themselves kill civilians and damage civilian infrastructure. A recent study of violence in Afghanistan showed that attacks by International Security Assistance Forces (ISAF) that harmed civilians reduced local support for ISAF, but equivalent attacks by the Taliban did not result in similar declines in support for the Taliban.

This response is due to intergroup bias: People are more likely to blame those they don’t know or who seem “other” and “foreign,” and give people with whom they more closely relate the benefit of the doubt. So ISIS’s brutality against the Syrian people may not offset coalition collateral damage enough to shift Syrian attitudes in favor of coalition forces. Even if people do not like the Islamic State, they might view the group more favorably than the coalition, view the United States as encouraging its rise or view coalition strikes against ISIS as providing indirect support for the Assad regime, which has killed more Syrians than any other group.

3) Attacking insurgents may actually strengthen their ranks.

Killing insurgent fighters is a sure way to encourage retaliation. If a group can signal strength through retaliatory attacks despite receiving heavy casualties, then local populations are more likely to view that group as strong. Some populations would see backing a strong group as the best way to protect their own interests. Strong groups are more likely to stick around and more capable of catching and punishing defectors. In certain contexts, these actions can be critical to group survival.

Signaling strength through violence might also produce fear that deters rival groups from attacking the Islamic State, or encourage a bandwagon effect that motivates new alliances. Given the large number of militant organizations operating in Syria — perhaps as many as 1,000 different groups — a stronger, more unified opposition could make stopping ISIS even more difficult, and could facilitate its spread to other countries.

4) A stronger insurgency is likely to result in more attacks on coalition forces.

Citizens in coalition home countries are likely to take notice of these signals as well. Military campaigns that appear unwinnable can reinforce political demands for coalition withdrawal. The result can undermine military efforts abroad and make it harder to suppress insurgent threats. During the Iraq War, for instance, public statements in the United States criticizing the war effort emboldened insurgent movements, which increased their attacks on coalition forces and led to more U.S. casualties.

So what’s the answer?

Do these findings suggest there is no place for a military solution in Syria? No, but they do indicate that to be successful (or at least not make matters worse) a military solution must coincide with an approach to conflict resolution that has considerable local buy-in. A strategy that increases engagement with Arab states, and with moderate Sunni populations in Syria to heighten local resistance and enhance intelligence gathering, could help increase the precision of coalition military strikes, minimize civilian casualties, and aid in organizing disparate opposition forces. This approach could also help encourage the formation of a viable political alternative to the Assad regime.

There’s a precedent for this approach. In 2006, the coalition initiated a process known as the Anbar Awakening, which sought to co-opt local Sunni tribes with aid and financial compensation to assist in the fight against al-Qaeda in Iraq (AQI). These actions, together with the 2007 “troop surge,” created a synergistic effect. The Awakening diminished insurgent ranks and revealed holdouts to U.S. forces, while the surge reduced sectarian violence and fostered the security conditions necessary for this process to succeed.

If there is military action in Syria in the future, this approach may also prove successful. We are not suggesting a U.S. ground war in Syria, but the notion that military might alone proved insufficient in Iraq, and that it was only through local collaboration that coalition forces were able to shift conflict momentum, are good lessons to keep in mind when crafting an approach to stop ISIS. While the Iraq and Syria conflicts are unique, they also display many similarities. Many of the groups now fighting in Syria initially emerged in Iraq — so examining the lessons learned from the Iraq War might be a good start in evaluating how to fight this one.

Emily Kalah Gade is a PhD candidate at the University of Washington. Joshua Eastin is an assistant professor of political science at Portland State University.