Daniel S. Markey is a senior fellow at the Council on Foreign Relations and the author of “No Exit From Pakistan: America’s Tortured Relationship With Islamabad.”

Last week, a U.S. drone strike killed Hakimullah Mehsud, one of Pakistan’s most bloodthirsty terrorists, in front of his family’s farmhouse in North Waziristan. In every respect, the logic behind the killing appears identical to that of past U.S. attacks against top Pakistan-based terrorists, including Osama bin Laden. Mehsud had American blood on his hands, and he would doubtless seize every opportunity to kill again. His death would be at least a temporary setback for the Pakistani Taliban, a loose collection of Pashtun militant groups, if only because it would have trouble finding a new leader as supremely murderous as Mehsud. Case closed.

In fact, the political and strategic circumstances of Mehsud’s killing are a lot more complicated. His death is a possible turning point. Yet it is not clear that Washington will use it to advance greater U.S. purposes in Pakistan. Handled poorly, this narrow counterterrorism success will come at a cost in bilateral relations, regional counterterrorism operations and the endgame of U.S. military operations in Afghanistan.

Unless the United States moves smartly, the killing of Mehsud is likely to have about the same implications for U.S.-Pakistan relations as the U.S. raid on bin Laden’s compound. As I learned during a research trip to Islamabad a week after bin Laden’s death in May 2011, the Pakistani national debate moved astonishingly quickly from shock to humiliation to anti-Americanism. After that, a series of crises over the rest of 2011 took U.S.-Pakistan relations close to a full rupture.

Today, Pakistani opposition politician Imran Khan is calling for his country to close supply routes to landlocked Afghanistan, as it did for half of 2012. Khan, like many Pakistanis, sees Mehsud’s death as an American move to sabotage a nascent peace process between the Pakistani Taliban and Islamabad. Senior ministers have voiced outrage over the strike, which came on the heels of Prime Minister Nawaz Sharif’s visit to Washington, where he made a point of publicly demanding an end to the U.S. drone campaign in his country.

From this perspective, at least the timing of this latest U.S. drone strike looks profoundly shortsighted. If, for instance, Washington had allowed the peace talks to move ahead, they almost certainly would have failed on their own. Mehsud’s core demands — for Pakistan to be administered according to Taliban-style law — cannot be reconciled with the nation’s constitution or with popular will. Sooner or later, that fundamental truth would have been exposed, just as it was in an earlier, collapsed peace deal between Islamabad and the insurgents who took over the Swat Valley in 2009. Because the Taliban overreached, the army won a broad political consensus to move in and crush the insurgency. U.S. officials might have let a similar process play out again, even if that meant not taking a shot at Mehsud.

Then again, there are good reasons to believe that U.S. analysts doubted that Pakistan’s government ever planned to turn on the Pakistani Taliban. In many ways, Islamabad seemed more inclined to temporize, perhaps by securing a new arrangement that would push the Taliban’s murderous activities into Afghanistan as U.S. forces head for the exits. Conversations with senior Pakistani intelligence officers lead me to believe this is almost exactly what some have in mind for other prominent terror groups based in Pakistan, such as the Haqqani network.

Such U.S. concerns are eminently reasonable, given the live-and-let-live arrangements that Sharif’s party appears to have struck with prominent anti-Indian terror organizations, including Lashkar-e-Taiba (the group responsible for the November 2008 attack on Mumbai). Moreover, Pakistan’s top general has, for several years, promised his U.S. counterparts a serious military campaign in North Waziristan, with no signs of delivery. Given this, the Obama administration can be forgiven for seeing little reason to hold fire on Mehsud to save peace talks, even if sabotaging those talks was not Washington’s main motivation.

Now that Mehsud is gone, the United States’ goal should be to drive a wedge between Islamabad and the Pakistani Taliban, deeper than the one between the United States and Pakistan. Judging by the shrill protests from Islamabad, this will not be easy. It is not, however, likely to be accomplished by waiting for the crisis to blow over. Instead, U.S. military and intelligence officers should approach their Pakistani counterparts with a plan to press their military advantage against the Taliban during its period of disarray. Although they may be rebuffed at first, Islamabad might soon reconsider if the Taliban directs its retaliatory fire against the Pakistani state, especially in Sharif’s home base of Punjab, as it has in the past. Then, in once again recognizing the need to confront a common enemy, Washington and Islamabad may find themselves allies of convenience, if hardly friends, and that would mean scoring a far greater victory than Mehsud’s death.