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The jungle redoubt of concrete bunkers and escape tunnels 200 miles (320 km) south of Bogotá was designed to withstand mortars and grenades in a direct assault by military forces. But the guerrilla leaders sheltering within had no chance against Operation Sodom, a predawn Sept. 22 raid in which 78 military and police aircraft — perhaps a fifth of the Colombian air force — swooped down on the Macarena mountain range and bombed the rebel stronghold into smithereens before the special forces moved in.

The use of such overwhelming force is almost unheard of in the annals of counterinsurgency, but no one was complaining about the result. Among the more than 20 guerrillas killed was the man Colombian authorities have feared for decades: Jorge Briceño, a.k.a. Mono Jojoy, "military commander" of the fierce but fading Colombian Revolutionary Armed Forces, or FARC. "This is probably the strongest and most important strike that we've made against the FARC," Colombian President Juan Manuel Santos, told TIME two days after the assault. Jojoy, he said, "was sort of a myth. Very cruel, very tough. We managed to kill the myth of the organization."

Now to finish the job. After 46 years of fighting FARC and cocaine cartels — their interests often overlap — Colombian forces say they are now tantalizingly close to ending the cycle of violence. That's thanks in no small part to more than $5 billion worth of U.S. aid over 10 years — Operation Sodom, for instance, used Black Hawk helicopters and state-of-the-art communications equipment. Along with military successes, Bogotá has also managed to run its economy better than most in its region, preserve a relatively strong if still unequal democracy and avoid the new brand of socialism propagated from its noisome neighbor, Venezuela's Hugo Chávez.

Santos, 59, who took office on Aug. 7, believes Colombia is on the cusp of becoming a major diplomatic and economic force in the Americas. Through booming sectors like oil, mining and tourism, he hopes it will this decade pass Argentina as Latin America's third largest economy, behind Brazil and Mexico. "South America is a continent that is now surging," says Santos. "We want to play a more important role in the region."

That would also suit Washington, which regards Colombia as a key ally: the U.S. hopes to relocate its regional antidrug and counterinsurgency operations to Colombian bases. U.S. officials also see Bogotá as a counterweight to Chávez. Santos is hoping these considerations will persuade the U.S. to agree to a free-trade agreement giving Colombian companies access to the American market. Such a deal could yield an economic bounty for a country where 46% of people still live in poverty.

But even as Santos pursues his ambitions abroad, he needs to vanquish FARC or get it to the negotiating table. In his previous job as Defense Minister, he presided over several successful operations against the insurgents. With FARC weakened — from almost 20,000 members a decade ago to about 8,000 today — his instinct is to go for the jugular. Santos told Colombian troops at a base near Florencia last month that he would keep after the guerrillas "until they no longer breathe."

In recent years, deadly military raids have choked off most of FARC's top leadership; its chief cocaine trafficker, Sixto Cabaña, was killed in a firefight with soldiers three days before Jojoy died. The group's political leader, Alfonso Cano, is still at large — but Jojoy may have been a more valuable target. He ran FARC's strongest unit, the Eastern Bloc, which in the late 1990s and early 2000s often routed Colombia's then threadbare army and controlled a Switzerland-size territory in the south. He was, says Bogotá-based security analyst Armando Borrero, "irreplaceable."

He was also generally reviled, not least because he championed FARC's strategy of kidnapping, and often killing, thousands of politicians and civilians — including presidential candidate Ingrid Betancourt in 2002 and three U.S. military contractors a year later. Under Jojoy, the Marxist guerrillas also developed an image as a drug-trafficking mafia in fatigues.

Alarmed by FARC's increasing power, Washington and Bogotá launched Plan Colombia, an antidrug program that was really a counterinsurgency effort: over the past decade, it has provided Colombia with military hardware, coca-fumigation aircraft and intelligence know-how. The assistance helped Santos' conservative predecessor, Alvaro Uribe, put FARC on the ropes. Perhaps the rebels' greatest humiliation came in 2008, when military agents, intercepting FARC communications, tricked them into freeing Betancourt, the contractors and 11 other hostages. Plan Colombia, Santos argues, is "the most successful bipartisan foreign-policy initiative that the United States launched in recent history." Santos was able to parlay his successes against FARC as Defense Minister to win the presidency by a landslide last summer.

But even if Colombians breathe easier for FARC's decline, some are already examining the price the country has paid for the military's victories. The military's dismal human-rights record was further blackened recently by a scandal involving the alleged murder of perhaps more than 1,500 civilians whose corpses soldiers dressed as guerrillas. The army also aided bloodthirsty right-wing paramilitary armies, which Uribe tried to demobilize, with mixed success.

Repairing the country's image is a task that likely comes easier to Santos than his predecessor. Santos' first success as President was mending fences with Venezuela. Uribe had exchanged verbal broadsides with Chávez over the latter's alleged support for FARC, and the two neighbors formally severed ties a month before Santos was sworn in. After his inauguration, Santos invited Chávez to a meeting in Colombia, where they re-established ties. Santos was courteous but firm. "I said, 'Don't pretend you are going to export your revolution in Colombia,'" says Santos. "But we are building mutual confidence." Those words, whatever Chávez made of them, are exactly what Washington wants to hear.
— With reporting by Dan Fastenberg / New York City

• Tim Padgett with John Otis / Florencia
• Military successes against a long-running insurgency give Colombia hope for an end to violence and the start of prosperity. But the job is unfinished