The men of Camp Blessing know they are bait. They dangle far from the formidable, heavily fortified perimeters of other U.S. bases in Afghanistan. Instead of the hundreds or thousands of troops that are in the large encampments, there are only a dozen Green Berets from what is known as Operational Detachment Alpha (ODA) 936 and a smattering of Marines. But they are dangling far from safety to attract a big catch. "This is Osama bin Laden's backyard," says the team sergeant. "And part of the solution to tracking him is having guys like us out here in isolated areas."

Several approaches are being tried to bring bin Laden and his lieutenants to ground. Pounding suspected sites is one, dramatized by the Pakistanis last week. Another is covert manhunts conducted by units like Task Force 121, the group of U.S. commandos that aided the capture of Saddam Hussein last year and that has recently been deployed to Afghanistan. And, increasingly, the job of persuading locals to provide intelligence on the whereabouts of al-Qaeda and Taliban leaders is being carried out in remote outposts like Camp Blessing along the border between Afghanistan and Pakistan, where small groups of U.S. special forces live side by side with local tribesmen. By extending U.S. influence and trading favors with tribal leaders, the military hopes to shake out the kinds of tips that will finally squeeze bin Laden into the open.

U.S. special-forces commanders recently gave TIME access to Camp Blessing, located in Nangalam in eastern Afghanistan. The camp is so secret that it doesn't even appear on U.S. military and embassy maps of bases in Afghanistan. Bin Laden reportedly was spotted within six miles of Nangalam a little more than a month ago. Villagers claim that a member of bin Laden's family wed a local girl farther up the Pesch River.

Camp Blessing, named for Jay Blessing, a U.S. Ranger sergeant killed in November, is a test of the "ink-spot theory of counterinsurgency," says Lieut. Colonel Custer (no first names allowed), the special-forces commander for eastern and southeastern Afghanistan. The idea is that as the U.S. brings stability to places like Nangalam, cooperation from locals will rapidly spread like ink through blotting paper. Since arriving three months ago, the men of oda 936 have launched numerous reconstruction projects, ranging from new footbridges to schools and clinics. Villages that are neutral or friendly benefit from aid. Those that haven't given up weapons or that abet the insurgents receive none. "We're generating the goodwill that engenders willingness to offer up information," says Custer, "and if bin Laden shows up, then we're ready to react."

But the Green Berets know they still have plenty of persuading to do. One night, the residents of Nangalam turned off the lights in their homes just before a rocket attack on the U.S. camp. "Someone knew those rockets were coming," says a commando, who cannot be named, like almost all the special-forces members who spoke to TIME for this story. For a base of its size, Camp Blessing is still tenaciously guarded. Observation posts lurk high on the ridges and are manned by Marines on 10-day tours. The Green Berets make sure their weapons-training sessions are loud and clear. "When the whole valley hears us firing 140 rockets in a day, they know we're not short of ammunition," says the team sergeant. "While we're a relatively small force here, if you want to come and mess with us, you're going to get hurt."

With its mix of inducements and force, ODA 936 is employing the same tactics long used by local chieftains. It's one thing to find the myriad "angry guys with beards" and kill them, says Custer, "but it's much better to co-opt them."

By establishing alliances with Nangalam's villagers, the Green Berets hope that intel will follow. Similar tactics worked for them in the 1960s in the Central Highlands of Vietnam. Last month 27 weapons caches were turned in to ODA 936 in Nangalam, more than anywhere else in Afghanistan. Once the troops' presence is established in the Afghan hinterlands, U.S. officers believe, the villagers will start to deny the terrorists sanctuary. Although one Green Beret says, "It's going to take dumb luck to stumble across Osama," the special forces are confident that someone will eventually give him up. "It may be the opium farmer whose daughter we airlifted to a hospital who thinks he owes us," says an officer who serves as the unit's intelligence chief, "and who comes in with something that we put with 18 other pieces of the puzzle, and we finally get a clear picture." They're still waiting for the prey to come into focus.

• Michael Ware/Nangalam