Three months after NATO's air war broke the Serbs' murderous hold on Kosovo it has become clear that Americans are being drawn toward a global role they tell pollsters and politicians they shun: that of the world's policeman.

The bitter disappointments of the Korean War discredited "police action" as an acceptable label for international intervention. No American president would acknowledge embarking on such an undertaking today. But today's world of fragmented national purposes and massive power imbalances encourages police actions to restore order in the neighborhood.

This should not be a matter of alarm in itself. Quick, effective international police actions that can stop massive murder and mayhem are certainly justified and needed. Kosovo fell into that category.

But there is cause for concern in the strategic incoherence, lack of candor and decline of creative diplomacy surrounding the use of American military firepower abroad for police purposes. These trends are all now evident in the confused aftermath of NATO's brief war in Kosovo.

The NATO powers deliberately set out not to change the political framework in which the Kosovo war started. Like patrolmen on the beat, they applied the force necessary to stop murders in progress and to chase the perps away from the victims.

Like President Bush in Iraq, President Clinton set out not to fight to the finish in Serbia. In the opening days of the conflict, Clinton's national security adviser, Sandy Berger, determinedly told reporters that there would be no Gen. Douglas MacArthur taking charge in Belgrade at the end of the fighting.

It was no longer an American option to defeat, occupy and remake the society of a military opponent, as MacArthur did in Japan, Berger suggested. The limited goals and means Clinton authorized were all that the public would tolerate or that were needed, Berger indicated.

The result is that Clinton now risks emulating Bush in Iraq in another respect: letting his successor and the world inherit the problems of dealing with broken but still defiant totalitarian regimes once denounced by an American president as evil incarnate.

Unfinished war is a distinguishing characteristic of world politics in the 1990s. It is true of Russia, in a different form: Both Bush and Clinton chose to bolster the Kremlin rather than pursue total victory when the Soviet Union collapsed. That choice, like the interventions in Iraq and Serbia, was right. But the policies and diplomacy that have followed do not equal the wisdom of the original decision.

The responsibilities and costs of looking after the affairs of a conflict's loser have become too great a risk in the electoral calculus of American politicians. This has led them into messy inconsistencies, the use of economic sanctions to punish populations for not deposing wounded regimes and other compromises inherent in dealing with partially defeated foes. But these options seem politically preferable in a time of shortened national attention spans, when electorates are interested in the pursuit of happiness, comfort and wealth.

Unfinished war and its untidy consequences are easier than taking on the responsibilities of full victory. Western governments use military cops on the beat to keep things quiet -- the repeated U.S. air raids in Iraq, the NATO peacekeepers in Kosovo -- while refusing to address the political framework that created the conflict, in the hope that something will turn up.

NATO governments continue to recognize Slobodan Milosevic's regime as the legal sovereign authority over Kosovo even as they make sure the Yugoslav regime cannot exercise its sovereignty. The United States adopted the same contradictory positions on Saddam Hussein and Kurdistan at the end of the Gulf War and still observes them.

This is a failure of diplomacy as well as imagination. Serbia threatens to harden over this winter into an intractable morass like Iraq unless NATO governments can pressure or induce Milosevic to step aside now. A deal providing him with guarantees against prosecution for war crimes in return for his going into exile and his regime's expiring may become necessary -- given the lack of any MacArthur-type alternative that would bring him to justice.

There is little in the background of George W., the physical son of Bush of Iraq, and Al Gore, the political son of Clinton of Serbia, to suggest that either would do things very differently as the next commander in chief.

Their rivals should draw them out on the use of U.S. forces for international police actions -- the gathering trend in national security that dare not speak its name.