IT’S BEEN 14 years since the United States, defying Russian obstruction in the U.N. Security Council, launched an air campaign to stop a tyrant’s bloody aggression in his own country. With U.S. support, the rebels of Kosovo, then a province of Serbia, were able to repel the army of Slobodan Milosevic and take control of the province. Critics warned at the time that U.S. intervention would sow chaos or empower radicals. Instead it paved the way for the democratization of Serbia, independence for a democratic Kosovo and, at last, the beginning of a reconciliation.

Hashim Thaci, onetime leader of the Kosovo Liberation Army and now the country’s prime minister, was in Washington last week to talk about an accord he reached with Serbian Prime Minister Ivica Dacic to normalize the two countries’ relations. The agreement is remarkable in both personal and political terms: Mr. Thaci was once a sworn enemy of Mr. Dacic, a close aide of Mr. Milosevic, and Serbia’s government has never acknowledged Kosovo’s independence. The agreement nevertheless calls for Serbia to accept the Kosovo government’s authority over all of his territory in exchange for extensive autonomy for areas where ethnic Serbs form a majority.

Struck on April 19, the deal seems to be sticking: A follow-up implementation agreement was reached last month. “It’s an unstoppable process at this point,” Mr. Thaci told us. “I have complete confidence that the implementation will go forward.”

The incipient settlement is an example of how Western intervention can stop a bloody and seemingly in­trac­table ethnic war — but also of how much effort is required. Since the fighting ended in 1999, NATO has kept a peacekeeping force in Kosovo, including U.S. troops; 760 American personnel are still there. The deal between Mr. Thaci and Mr. Dacic was brokered through the tireless diplomacy of European Union foreign policy chief Catherine Ashton, who oversaw 10 taxing rounds of negotiations.

Fortunately Ms. Ashton had something valuable to offer: the prospect of eventual E.U. membership for both countries. Thanks to its decision to come to terms with its former province, Serbia will likely be given a date this month by Brussels for the opening of accession talks, while Kosovo will be invited to begin work on an association agreement. Kosovo would also like to join NATO, which is one reason Mr. Thaci was in Washington: He was hoping the Obama administration will press the alliance to take preliminary steps toward admitting his country.

The United States should support that ambition and also press countries that have not yet recognized Kosovo, including several of its neighbors in southeastern Europe, to do so. But the Obama administration would also do well to take a lesson from this history. Limited U.S. military interventions, accompanied by a sustained follow-up and vigorous diplomacy, can save lives and stabilize troubled regions — even when Russia and the U.N. Security Council don’t approve.