ADDIS ABABA, Ethiopia -- "Get it done quickly and get out." That, says a senior U.S. diplomat here, was the goal of the little-noticed war that Ethiopia has been fighting, with American support, against Islamic extremists in Somalia. But this in-and-out strategy encounters the same real-world obstacles that America is facing in Iraq and Afghanistan.

Conflict is less the problem than post-conflict. That's the dilemma that America and its allies are discovering in a world where war-fighting and nation-building have become perversely mixed. It took the Ethiopians just a week to drive a Muslim radical movement known as the Islamic Courts from Mogadishu last December. The hard part wasn't chasing the enemy from the capital, but putting the country back together.

"The Ethiopians are looking for an opportunity to exit, but not until they are confident that the security environment will prevent a return to chaos," says a State Department official who helps oversee policy for the region. And in Somalia, a backward country that has seen 14 governments since 1991, that process of stabilization will be anything but easy.

The Somalia war comes up during every stop of a tour of the horn of Africa with Adm. William Fallon, the new head of U.S. Central Command. In 2002, Centcom established a regional outpost in the dusty port city of Djibouti, at the entrance to the Red Sea. It now has about 1,500 U.S. military personnel there. Some of them are out digging wells, building schools, vaccinating goats and otherwise "waging peace," as a spokesman there explains. That's the nation-building side.

The Djibouti base also provides logistical support for U.S. Special Forces teams that are hunting down what's left of the al-Qaida terrorist cells that bombed American embassies in Kenya and Tanzania in 1998.

Because Somalia provided a haven for al-Qaida, it was a special target after Sept. 11, 2001. But the Bush administration, remembering the disastrous 1993 humanitarian intervention there, was wary of getting involved directly. Initially, the CIA paid Somali warlords to hunt down al-Qaida operatives. But the warlords didn't catch many terrorists and, perhaps worse, the payoffs added to an anarchic situation that led many Somalis to turn to the Islamic Courts for protection.

The Somalis were mercenary but unreliable. One official recalls how the CIA distributed matchbooks in Somalia offering a $10 million reward for the capture of Osama bin Laden. The Somalis complained that they were being cheated because a CIA Web site was offering a $25 million reward.

The bounties to the Somali warlords "at the time appeared to be the only viable option given our lack of access," says an intelligence official back in the U.S. The secret CIA program was terminated in 2006.

Ethiopia, fearing the establishment of a radical Muslim government on its eastern border, began planning its military intervention soon after the Islamic Courts took control in Mogadishu in June 2006. At first, Centcom cautioned the Ethiopians against invading. But after 10,000 Ethiopian troops surged across the border on Dec. 24, they received U.S. overhead reconnaissance and other battlefield intelligence.

Next came an Ethiopian-American pincer strategy: In January, after Muslim fighters had fled Mogadishu, the U.S. launched two devastating air attacks by AC-130 gunships. A senior al-Qaida operative named Abu Talha al-Sudani was probably killed in these coordinated attacks, a U.S. official said. Overall, about 8,000 Muslim fighters were killed in the brief war, while the Ethiopians lost just 225 dead and 500 wounded.

A successful proxy war, from the American standpoint. But then what? The Ethiopians began pulling out their troops almost immediately, and by March, the Muslim radicals were threatening to regain control of Mogadishu. Ethiopian troops stormed back and crushed the Muslim rebels once again. The Ethiopians have now concluded that they can't withdraw completely anytime soon; they must instead stay and train a friendly Somali army that can support the pro-Ethiopian "Transitional Federal Government."

The Ethiopians are hopeful they can forge a reconciliation among Somali clan leaders. Meanwhile, the Ethiopians are looking for cover from an African Union force they hope will eventually total at least 5,000 soldiers; so far only about 1,800 soldiers from Uganda have shown up.

It's like Iraq and Afghanistan, in other words. A decisive military strike has destroyed one threat. But what's left behind, when the dust clears, is a shattered tribal society that won't have real stability without a complex process of political reconciliation and economic development.

There's no turning back now, says a U.S. diplomat, but he cautions: "Anyone working in Somalia has to have developed a certain humility about our ability to pick leaders from clans and sub-clans."