On Friday, the Pentagon confirmed that American airstrikes in Somalia last week had succeeded in killing Ahmed Abdi Godane, the leader and co-founder of the al Qaeda-linked Islamist group al-Shabab. “Removing Godane from the battlefield is a major symbolic and operational loss to al-Shabaab,” Pentagon Press Secretary Rear Admiral John Kirby said in a statement.

The symbolic loss may be bigger than the operational loss, however. Targeted airstrikes or special-operations raids aimed at “taking out” leaders of terrorist organizations are arguably the most critical component of the Obama administration’s light-footprint counterterrorism strategy, which my colleague Stephanie Gaskell summed up at Defense One as: “partner up with local nations, build strong intelligence for targeted strikes and keep no U.S. boots on the ground.” But the popularity of "decapitating" militant organizations rests on an assumption: that removing an extremist group’s leadership degrades or diminishes the group as a whole—making it less violent or causing it to collapse altogether. Whether this assumption is correct is by no means a settled question, and the history of terrorist and other violent groups whose leaders have been killed or captured leaves reason for doubt.

There have been high-profile cases in which the death or capture of a militant group's leader has significantly weakened the organization. The Kurdistan Workers' Party, for example, scaled back its attacks in Turkey following the 1999 apprehension of its leader Abdullah Ocalan; analysts have also credited "leadership decapitation" with dealing decisive blows to Japan's Aum Shinrikyo and Peru's Shining Path. On the other hand, Israel has targeted Hamas leaders for years, and the Palestinian group appears nowhere near dissolving. Bloody succession struggles within Mexican drug cartels following the removal of kingpins demonstrate that the approach can actually increase a group's violence.

More systematic studies of leadership decapitation only confirm that the evidence for its success rate is mixed. In 2009, for instance, Jenna Jordon of Georgia Tech examined 298 instances of terrorist leaders being targeted between 1945 and 2004. According to her findings, organizations that experienced a loss of leadership in many cases remained active—as measured by their inclusion on the U.S. State Department's list of Foreign Terrorist Organizations—longer than organizations that collapsed for other reasons. "Organizations that have not had their leaders removed are more likely to fall apart than those that have undergone a loss of leadership," she concluded.

But different measures yield different conclusions. Examining 90 insurgent campaigns from 1975 to 2003, RAND Corporation's Patrick Johnston found evidence in 2012 that removing an insurgent group's leadership increased a government's chances of victory in counterinsurgency campaigns and decreased the violence of the conflict. A forthcoming paper from Northeastern University's Max Abrahms and the University of Michigan's Philip Potter reports that leadership decapitation may increase civilian casualties. Militant groups in the Afghanistan-Pakistan region, Abrahms and Potter discovered, became “significantly less discriminate in their targeting choices”—in other words, more likely to target civilians—after high-level militants were killed in drone strikes.

“The leadership can actually have a restraining effect on lower-level members,” Abrahms tells me. For example, al-Qaeda’s current leader, Ayman al-Zawahiri, has instructed his rank-and-file to "avoid collateral damage," and famously split with ISIS in February in part over the group's ruthlessness. Abrahms speculates that in that sense, decapitation could indirectly and over time shorten the lifespan of a terrorist group, since such organizations usually lose popular support when they inflict high civilian casualties. But that means counterterrorism officials are making a grim calculation: Taking out terrorist leaders may benefit civilians in the long term, but in the short term it only endangers them further.

The efficacy of removing terrorist leaders depends in part on the nature of the group targeted. In her 2008 book How Terrorism Ends, Audrey Kurth Cronin of George Mason University identified leadership decapitation as one of several factors that have historically been involved, sometimes in combination, in the demise of terrorist organizations—with negotiations, loss of popular support, and repression among the others. “Those that have ended through decapitation," she has written, "have tended to be hierarchically structured, young, characterized by a cult of personality, and lacking a viable successor.” In her own study, Jordan found that religious organizations "are highly resistant to leadership decapitation."

So what kind of an organization is the suddenly leaderless al-Shabab? Kenneth Menkhaus, a political-science professor at Davidson College who has studied the group, tells me that Godane was clearly the “driver of al-Shabab strategy and policy,” mainly because of a bloody purge Godane conducted against potential rivals in the summer of 2013. But it’s also possible that the group has become more decentralized since an African Union-led offensive beginning in 2011 drove al-Shabab out of major cities in Somalia. If far-flung cadres in the countryside have been operating autonomously, Godane’s death may not change the organization much at the local level.

In fact, as Menkhaus notes, “Shabab has already experienced decapitation” and managed to recover. After a U.S. airstrike killed the group’s then-leader Aden Hashi Ayro in 2008, “Godane stepped in and it was business as usual.” Indeed, it was after Ayro’s death, and while Godane was consolidating his position, that al-Shabab carried out its highest-profile attack outside Somalia: the assault on the Westgate mall in Nairobi, Kenya, which killed almost 70 people. Al-Shabab has already namedGodane's successor, and the Somali government has cited intelligence that the group could be planning attacks on educational and medical institutions.

For all these reasons, Cronin tells me, al-Shabab does not fit her model of a group likely to die by decapitation. “I don't see a 'cult of personality'—more like a decentralized, fractious jumble of competing individuals, clan loyalties, locals vs. foreigners, executions and murderous in-fighting,” she writes in an email.

Al-Shabab’s longevity could also depend on an amnesty that the Somali government offered to fighters in the wake of last week's airstrike, Menkhaus says. The amnesty could take advantage of any internal fissures that have opened up over the group’s future direction in the wake of Godane's death. Widespread defections could be yet another blow to al-Shabab.

If al-Shabab leaders accept the amnesty and try to take part in a power-sharing government, Menkhaus says, the U.S. will have to consider which former terrorists it is willing to deal with as part of its cooperation with the Somali government. "Who could we live with? And where do we say, 'no way?'" he asks.

These kinds of questions will only grow more urgent; the U.S. now appears to be targeting ISIS leader Abu Bakr al-Baghdadi, and has killed members of his inner circle in Iraq. Targeting top terrorists may be a fast, no-boots-on-the-ground way to avenge the deaths of innocents. But it won't necessarily make ISIS—or any extremist group, for that matter—go away.