Americans have killed hundreds of people over the past two years in aerial-drone strikes in Pakistan, an unlucky group that includes women, children, and a whole lot of low-level militants. But every once in awhile, the U.S. military hits a big target. On Aug. 22, his name was Atiyah Abd al-Rahman, a figure known by few people in this country but who was immensely powerful within the terrorist group al Qaeda.

Forget Osama bin Laden, the so-called terrorist mastermind. In real life, he was the guy watching videos of himself in a room in his Abbottabad compound; meanwhile, al-Rahman was making plans.

“He was the general manager of al Qaeda,” Marc Sageman, author of Understanding Terror Networks, tells me. “He was running it.” The death of al-Rahman, a 38-year-old Libyan who had been living in Waziristan, the tribal region of Pakistan, is “far more devastating” than that of bin Laden, Sageman says, explaining that bin Laden was a symbolic leader, but al-Rahman “was giving very specific directions for operations.”

Obama supporters say the killing of al-Rahman is the latest in a string of White House successes against the terrorist group and further proof that the laserlike approach, with its reliance on drone strikes, is the right one. In this way, CIA officers are thinning the ranks of al Qaeda and gradually making them obsolete: Or, as Defense Secretary Leon Panetta said last month, Americans are “within reach of strategically defeating al Qaeda.”

Not everybody is so optimistic, though. Critics of the Obama White House say that the fallout from the drone strikes in Pakistan has been far worse than any gains made in fighting the terrorist group: Indeed, in Pakistan al Qaeda is more popular than the United States, according to some opinion polls, and terrorists have found the drone strikes a powerful tool for recruiting new suicide bombers.

Moreover, these critics argue that al Qaeda has never been about numbers, which even at its peak had only a limited membership, and so thinning the ranks does little, and taking out its leaders, as the lethal strikes have done in Pakistan, does not necessarily mean the death of the organization. Research shows that when a terrorist group loses its leader, it is destroyed less than one-fifth of the time; in the other cases, the members of the group find another person to act as an authority figure and simply carry on with their work.

Still, al-Rahman was bad. He joined al Qaeda when he was a teenager and over the years helped to broker deals between al Qaeda Central and like-minded groups in Algeria, Iraq, Iran, and other countries. And it is also true that, as Sageman points out, once you take away the numbers, you do not have much of an organization. In other words, “leadership decapitation,” as it is known, can work.

It is too soon to tell what kind of impact al-Rahman’s death will have on the terrorist group, but one thing is clear: the success of the strike in Waziristan, like the one against the compound in Abbottabad on May 2, will embolden those in the White House who support a targeted approach against terrorists, even when the strikes are carried out independently and without prior consent from authorities in sovereign nations such as Pakistan. “We have a winning strategy right now, and we’re going to continue till all those guys are dead or completely defanged,” Sageman says.

Now that al-Rahman is gone, CIA officers in Langley, Va. and in stations around the world will double down on their efforts to pursue their other targets. These include al-Rahman’s boss, Ayman al-Zawahiri, who became bin Laden’s successor earlier this year and may be living in the border area between Pakistan and Afghanistan; a religious scholar named Abu Yahya al-Libi, who appears frequently in al Qaeda videos; and radical cleric Anwar al-Awlaki, who was born in the United States and is now reportedly hiding out in Yemen.

In the meantime, CIA officials have reason to celebrate, since by almost any account the death of al-Rahman is significant. “Al Qaeda has not signed a surrender, and nor will it,” says Sageman, “but their ability to launch operations is diminished.”