Pull them out. That’s what many Americans these days want to do with U.S. troops. That’s why they reacted in such mixed fashion to President George W. Bush’s announcement that U.S. soldiers might stay in Iraq to the end of his second term.

After all, many Americans are coming to believe that posting soldiers to spend years defending a beleaguered Muslim population in some dangerous backwater is a suicide mission. What’s more, the reasoning goes, the locals will make you look bad for even trying.

This week I am visiting a place that may disprove all those ideas – and in the end provide a powerful precedent for Bush’s Iraq plan. It is Kosovo, the conflict-ridden southern region of the old Yugoslavia. As far as ethnic battlegrounds go, Kosovo is right up there. The Albanian Muslims and the Orthodox Christian Serbs have been at one another for almost a millennium.

In muddy Pristina, Kosovo’s capital, U.N. officials and NATO forces oversee a population that includes gun-happy thugs, transient Romanian drug traffickers, and disgruntled grandmas. Yet everyone involved somehow in this terrible neighborhood, even the Albanians on Bill Clinton Boulevard, seems to want the 1,600 or so Americans troops to stay. Sometimes they don’t ask. They insist.

“There will be no more war in the Balkans,” Ardian Gjini, a cabinet member in Kosovo’s provisionary government, said in a meeting this week in Pristina. “The U.S. presence is why.”

On the off-chance that Donald Rumsfeld or the rest of the Pentagon will be reading his quote later, Gjini throws out a second reason for Americans to stay. “It’s cheaper to keep people here than to redeploy them.”

Half a decade ago Gjini was a gun-toting freedom fighter – a terrorist, if you like. Now he finesses his point as neatly as a French diplomat: “Kosovo does not want to become independent of the world,” he concludes. “It wants to become independent of Serbia.”

Down the road, Fatmir Sejdiu, the president of Kosovo, is also enthusiastic. Sejdiu, an Albanian Kosovar, welcomes Americans to an office adorned with a photograph of Mother Theresa and a NATO flag: “We have a special commitment to NATO and its value,” he says, and tells visitors he has a sibling, a doctor, in New York.

To understand how Kosovars became so America-happy, it helps to recall the history. In the late 1990s Serbian leader Slobodan Milosevic, a Saddam-like despot, ordered soldiers and irregulars to undertake their boldest effort at ethnic cleansing yet, killing and forcing more than a million Kosovars from their homes. NATO bombed Serbia’s capital, Belgrade. This right-wing neocon intervention was led by people named Bill Clinton, Madeleine Albright, and Tony Blair.

After Milosevic capitulated, a NATO force for Kosovo, KFOR, and UNMIK, the U.N. entity, moved in. The U.S. troops are only a fraction of the more than 15,000 here in Kosovo.

More than six years later, this thug-state is hardly de-thugged. KFOR trucks patrol the streets; people are accustomed to the long, dark pause between the moment the electricity fails and the moment the generator kicks in. Walls of churches are decorated with engravings of dead teens, the casualties of drive-by shootings.

Albanian Kosovars and the Serbians here and in Belgrade are still at odds over Kosovo’s future, with the Albanians demanding political independence and Belgrade pushing for some narrower form of autonomy. Still, there is a sense in Pristina that an allied-brokered political agreement is imminent, and that Kosovo is close to peace now. Inter-ethnic crime is down and Albanian Kosovars are learning to govern.

What’s interesting about this powder keg, at least to someone thinking about Iraq or Afghanistan, is the broad enthusiasm for the U.S. soldier. I’m traveling with a U.S. foundation, the German Marshall Fund, on whose board I sit. We also visit Belgrade – a Serb city where yellow construction equipment is still pushing around rubble from the months of bombs that NATO dropped on the city.

We discover that the experience has not damped the faith in the GI. How long must the U.S. stay in Kosovo, we ask? “At least 10 or 15 years,” says one Serb official. Can NATO go? “Not now,” says another. Firmest of all is the foreign minister of Serbia and Montenegro, Serbian Vuk Draskovic, who says: “Americans must stay there.”

Serbians and Kosovars long for entry into the European Union; that’s their plan for economic stability. But they look to the U.S. for military support, and, one senses, a cultural and economic presence.

One member of our group, thinking of the “troops-out” mood at home, asks whether Europeans soldiers might replace American ones in Kosovo. No, the reply comes again. “Europeans are good fellows,” one official says. “They operate in two speeds. Slow and slower.”

I can almost hear Rumsfeld bark back: It is machines and satellites, not vulnerable flesh, that the defense secretary wants to see policing the globe now. You can also make a case that keeping military babysitters for years in places like Kosovo merely inspires the locals to continue their lethal squabbles.

Still, the former Yugoslavia is worth looking at twice.

People in the U.S. just now may doubt the value of flying the flag in these places. But in Kosovo and Belgrade, they don’t.

Miss Shlaes is a columnist for Bloomberg News.