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Handoff: Petraeus may be passing over day-to-day command in Iraq to others, but he’ll have a lot to contribute in his new role.

Gen. David Petraeus left Iraq last week with proper fanfare for his success in dramatically reducing the violence that had steadily engulfed the country until late last summer. At the end of October, he’ll take the helm of the four-star Central Command that oversees U.S. military affairs in all of the Middle East and South Asia. His new to-do list will be long and complex. The general will no doubt be applying a number of important lessons from Iraq in his new command. They aren’t necessarily the lessons most people think, but they just might be the lessons that America—struggling to contain a growing two-country war in Pakistan and Afghanistan and locked in a tense regional showdown with Iran—urgently needs to learn.

The key to the success in Iraq was, first of all, to correctly diagnose and address the fundamental problem. It sounds obvious, but it hadn’t been done by the previous commander or the White House policymakers. “The job of the leader is to get the big ideas right,” Petraeus told me during a Sept. 2 interview in his office in Baghdad’s Green Zone. When he arrived in Iraq in January 2007, he put together a top-notch multidisciplinary study group of military, academic and diplomatic experts to analyze the war’s current state in depth and map out a sophisticated approach. They concluded that the war had become primarily a “communal struggle”—a polite term for civil war. The resulting campaign plan called for all efforts—political, military, and economic—to focus on achieving political accommodation. Previously, U.S. troops had been applying counterinsurgency tactics but in a localized, isolated, and temporary fashion, rather than in an integrated, countrywide approach.

When Petraeus takes the reins at CENTCOM, he’ll need to take a similar long, hard look at Pakistan’s border region and Afghanistan to arrive at the same fundamental diagnosis of the problem. As in Iraq, he is likely to conclude that the solution lays not in merely pumping more troops into the region but rather in how those troops are used. Nor, with apologies to Bob Woodward, will there be some silver-bullet technical solution to kill or capture the al Qaeda leadership. Troop numbers and technology were not the key factors that turned the tide in Iraq.

The Mesopotamian lessons that will be most useful in the South Asian conflict derive from Petraeus‘s famous counterinsurgency manual, which emphasizes a “population-centric” approach. In Iraq, his command placed top priority on securing the population, meeting its needs, and shoring up the legitimacy of the government versus the insurgency. Engineers built walls and soldiers erected checkpoints to protect the population and keep out car bombers.

Much has been made of the coalition’s recent successes against al Qaeda in Iraq. But only in a very focused way did Petraeus take an “enemy-centric” approach to the terrorist organization. Killing the bad guys worked because the killing was more discriminate and the hardcore elements were separated from the rest of the insurgency and the population support base. Thanks to new human intelligence gained from the population and former insurgents, these operations were more precisely aimed at small numbers of “irreconcilables.” Biometric devices helped create a computerized, shareable registry of possible insurgents, which led to more accurate targeting. Other technical means then allowed rapid targeting of entire cells, but it was human intelligence that ensured the targets were the right ones. Then, U.S. and Iraqi troops held the areas after counterterrorist operations, unlike in the past.

Toward the mass of the Sunni insurgency, Petraeus adopted a new strategy. “We can’t kill our way to victory,” he was fond of saying. He sought instead to convert those who were fighting—bringing the “reconcilable” insurgents in from the cold.

The obvious parallel in his new role is to the Pashtun nation that straddles the border of Pakistan and Afghanistan. Pashtuns form the support base for the Taliban insurgency, which in turn gives sanctuary and support to the much smaller al Qaeda network. The United States and NATO need an approach that wins over the Pashtuns, looks for Taliban converts, and uses the resulting intelligence in a very focused counterterrorist campaign against al Qaeda. Unfortunately, this is contrary to the dominant thinking in the policy debate. Many in Washington are pressuring the administration and Pakistan to “get tough” in the tribal areas when in fact they need to “get smart.”

Given what he has achieved in Iraq, Petraeus brings unique credibility to the “get smart” crowd. And unlike many U.S. generals who see war in narrow military terms, Petraeus lives and breathes the Clausewitzian maxim that “war is the conduct of politics by other means.” He understands better than anyone that each time an errant bomb kills innocent Afghan or Pakistani villagers, the coalition loses support in those countries and at home.