It took less than a year after the Sept. 11 attacks for the first phase of the war in Afghanistan to conclude with an American victory. But unless U.S. policy-makers adjust their strategy, it won't take long to "lose the peace."

It's true that the military situation in Afghanistan is, for now, extremely favorable. Approximately 7,000 U.S. soldiers are deployed in the country, along with 5,000 peacekeeping troops in the International Security Assistance Force, which maintain order in the capital city of Kabul. The al-Qaeda forces were forced to disperse and go into hiding. Most of them, according to U.S. intelligence officials, fled into Pakistan. The Vietnam-like "quagmire" that critics predicted hasn't materialized.

But while the military picture is bright, the political one is murky. Although American troops have captured or killed roughly half of the top 30 Taliban leaders, they have not captured Mullah Mohammed Omar, its supreme leader, or many of his chief lieutenants. And they're not getting much help from certain Afghans, such as the ethnic Pushtuns that live in southeastern Afghanistan, who refuse to cooperate in hunting down these leaders. Indeed, some Pushtuns, particularly those in the Taliban's former strongholds in southern Afghanistan, helped them escape.

That any of the Pushtuns would help the Taliban may seem puzzling, especially to those who champion a greater role for American forces there. Even now, U.S. officials are debating a plan to expand the international security force beyond Kabul to boost security. Defense Secretary Donald Rumsfeld doesn't like the idea, pointing out that it would interfere with work already being done by U.S. security forces in Kabul.

But there's another reason. Years of continuous warfare, which began long before we arrived on the scene, have created a complex constellation of regional, tribal and ethnic leaders. We can't expect these leaders to rubber-stamp foreign plans for "nation-building" or bow down to a Kabul-based central government if they believe it threatens their personal power.

Besides, the Karzai government is under intense public pressure to distance itself from the U.S.-led war effort, which is becoming more unpopular among southern Pushtuns, the former power base of the Taliban. Matters weren't helped earlier this summer by a "friendly fire" incident, in which an American gunship reportedly killed more than 40 Afghans (including 25 at a wedding ceremony), sparking an anti-U.S. demonstration in Kabul.

The highest priority for the U.S. military at this phase is to destroy Islamic extremist groups that threaten to destabilize Afghanistan. Al-Qaeda and Taliban forces, which suffered heavy losses, have dispersed into small contingents. Ferreting them out requires the use of special forces backed by precise air strikes, rather than large conventional ground units.

These forces should work closely with the CIA's paramilitary units and the Afghan central government to cultivate intelligence sources among the local populations to help identify, locate, and capture fugitive al-Qaeda bands and the top Taliban leadership. Such intelligence is critical if we want to prevent any more "friendly fire" incidents from taking place.

Once Mullah Omar is captured or killed, American forces should turn primary responsibility for hunting Taliban leaders over to the Afghan government and focus almost exclusively on eradicating al-Qaeda units, which pose a greater threat to U.S. interests. By concentrating on hunting foreign terrorists rather than Afghans, the United States can reduce the risk of accidentally killing civilians and improve the chances of gaining local support for the war effort.

And while ultimate responsibility for guaranteeing a peaceful future belongs to the Afghan people, America can help the Afghans help themselves. The United States should continue to assist in training the Afghan national army, for example, and provide expertise to help the Afghan government build necessary infrastructure and civil institutions.

But we need to know when to stop. That means the United States shouldn't commit combat troops to an open-ended peacekeeping mission or a nation-building experiment. U.S. troops are needed to eliminate the terrorists and crush rogue regimes that support them, not to undertake vague missions to win hearts and minds. Leaving large numbers of U.S. troops inside Afghanistan to pursue political feel-good missions is a sure way to turn victory into defeat.

James A. Phillips is a research fellow specializing in Middle Eastern affairs in the Davis Institute for International Studies at The Heritage Foundation.