THERE is glee in the voices of UN officials. NATO commanders are relieved they are no longer limited to ''pinprick'' attacks. And Western diplomats are sounding more like ''make my day'' Clint Eastwood than ''make peace'' Jimmy Carter. NATO resumed airstrikes Sept. 5 after Bosnia Serbs failed to remove all heavy weapons from around Sarajevo. Officials promised the strikes would last for at least three days and would immobilize Bosnian Serb forces by targeting roads, bridges, and power stations in nearby Serb-held territory. ''This is different,'' says one euphoric Zagreb-based UN official. ''This is like the Gulf war.'' In the course of a few weeks and a few hundred bombing runs, the troubled UN mission in Bosnia has been transformed from the Western world's stepchild to its proud, All-American son. For now, the unprecedented US-European division over Bosnia that has handicapped the mission for years has been replaced by unprecedented support for massive airstrikes. In the end, analysts say, it was shoot or be shot at during a humiliating UN withdrawal. And for now, much sanitized, relatively low-risk aerial ''shooting'' is playing well in Omaha, Liverpool, and Marseille. ''It's giving everyone an opportunity to fulfill their [domestic] agendas,'' says the UN official. ''The Americans can take credit for whatever happens, the French can claim they liberated Sarajevo, and the British can be on the winning team.'' Airstrikes have begun a more or less win-win situation for the US, British, and French leaders. If the strikes fail to fully cow the Bosnian Serbs, President Clinton can embrace lifting the UN arms embargo on the Muslim-led Bosnian government - taking away a powerful political weapon from presidential rival Sen. Bob Dole (R) of Kansas - and justify sending US troops to Bosnia to withdraw UN forces. Airstrikes have allowed Britain, the most vocal opponent in the past to bombing, to reduce the number of peacekeepers it has at risk on the ground. All UN peacekeepers in Bosnian Serb territory - including 300 British in the surrounded Muslim enclave of Gorazde - have been withdrawn. The possibility of the Serbs turning them into ''human shields'' has been minimized. Meanwhile, French President Jacques Chirac has been able to talk tough on Bosnia while deflecting attention from French nuclear testing in the South Pacific. The UN's new French-led Rapid Reaction Force, a well-armed 10,000-man unit whose guns have been pulverizing Serb positions along with NATO jets, could lead a withdrawal from Bosnia just as easily as it could break the siege of Sarajevo. ANALYSTS say British and French troops are better positioned for a safe withdrawal from Bosnia than they have been in several years - a key factor in getting the French and British to agree to long-running US calls for heavy airstrikes. ''It's a scenario with an endgame for the West,'' the UN official says. ''Total failure means withdrawal, and success means peace.'' But critics warn that the unprecedented Western unity may be short-lived. The only thing unifying the Western powers is expediency, they say. Desperate to settle an ugly war that has become a domestic embarrassment in the US, Britain, and France, Clinton, Prime Minister John Major, and Mr. Chirac are allies now, but may be rivals again later. The deaths of a large number of British or French soldiers, or American pilots, could quickly lead one of the three leaders to back off. Clinton is eager to use NATO military might to force a peace deal now or pull the UN out before next year's election. Major, fresh from winning a leadership struggle in his own party, and Chirac, facing increasing criticism for his focus on foreign policy, may be less willing to take big risks and solve Bosnia American-style - quickly. ''Major and Chirac have different agendas from Bill Clinton,'' says Dan Nelson, head of the international relations program at Old Dominion University in Norfolk, Va. ''Clinton wants to get this off the front page while Major and Chirac are both in the settle-back mode.'' Time is what the Bosnian Serbs think is on their side, Mr. Nelson says. Their only hope is that the sudden, rare unanimity among the Western allies will, just as it has in the past, dissipate as quickly as it formed. ''The US is still pulling and tugging the British and French along,'' Nelson warns. ''Inter-allied discord is going to be the key issue here.''