IT IS day six of Operation Desert Regime Change and the doubters have been put to flight. Saddam Hussein is missing, presumed dead; Iraqi forces have crumbled, civilian casualties are limited.
Iraqis greet troops from the United States as liberators, allied forces bury their fears that every Iraqi face hides a suicide bomber, and the siege of Baghdad looks nothing like the siege of Beirut.
But if the military victory falls into place, and Tony Blair, the Prime Minister, and George Bush, the US president, are hailed as heroes on the home front, how rapidly can rifts be healed in a divided world?
Relations with key allies have been badly jostled in the wake of Mr Bush’s single-minded determination to oust Saddam. Old dividing lines in the United Nations, NATO and the European Union have been wrenched apart.
Already, the sides are manoeuvring to paper over their differences. Dominque de Villepin, the French foreign minister, has spoken of his love for the US, between the jibes at young democracies and old Europe.
Mr Bush, at the prodding of his father, talks of his friendship for France, and Germany. China is well aware of its lucrative trade relationship with the US, and Russia of the dollars it needs to run its space programme.
If the US and Britain win their second war in the Gulf in the lop-sided manner they are praying for, it will be left to Colin Powell, the US Secretary of State, to put the world back together again.
Mr Powell launched a last effort last week to persuade the United Nations Security Council to vote to endorse military action. As the man who persuaded a reluctant White House to go to the UN in the first place, his personal credibility is already on the line. Critics inside the Bush administration already say his diplomatic skills have failed the test.
The vote, however, is also vital to a new post-war consensus. The UN may be able survive a veto by France alone, dismissing it as a case of Gallic obstinacy. Opposition from Russia and China will be harder to bridge.
International acceptance of war will depend heavily on how US forces manage its aftermath. The Pentagon now describes a long-term occupation of Iraq, of up to two years; US forces will be forced to act as middle man between Turks and Kurds, Shia and Sunni Muslims.
Washington will have to fend off suspicion, meanwhile, that it has at a stroke vastly expanded its military and strategic influence in the oil-rich Middle East.
European nations were becoming restive about growing US power before Mr Bush took office, says Andrew Kuchins, of the Carnegie Endowment for International Peace in Washington.
"My view is that we’ve handled this diplomatically in a very clumsy way, and we’ve really painted ourselves in a box. And I think we’ve needlessly alienated a lot of key allies and partners," Mr Kuchins said.
Some Arab commentators, and many Iraqi exiles, say US forces will be welcomed in Iraq as long as they keep their stay short. King Abdullah of Jordan is said to be hoping for a week of war followed by a US withdrawal within three months.
Whether Washington makes any genuine effort to reach a settlement in the Israeli-Palestinian dispute - as did the first Bush administration in the wake of the 1991 war - may be a key to building and keeping good will.
The war will leave a US-occupied Iraq with a 730-mile border with Iran, which has supported groups such as Hezbollah and Hamas.
Iran’s Islamic clerics in particular still see the US as an enemy second only to Israel. Mr Bush for his part has listed Iran in his famous "Axis of Evil".
On the international scene, it is NATO in particular that threatens to become "collateral damage". The Iraq crisis has taken the dull debates over NATO’s job in a post-Cold War world and put them into stark relief. NATO’s current military role has been limited to "protecting Turkey" - and even that was thrown into confusion since Turkey, for now, has rejected any role in the war.
Only days after Lord Robertson, the secretary general of NATO, discounted any threat to remove American forces from anti-war Germany, a top US commander confirmed a likely shift into the more friendly territory of new eastern European NATO members.
The UN, for its part, "is much, much larger than the Iraqi crisis," its secretary general, Kofi Annan, said this week.
But suspicion of the UN among Republican circles in the US has only grown. The worst-case scenario, analysts say, could see the UN relegated to a 1 billion-a-year debating society, or returned to the decades-long stalemates and theatrics of the Cold War.
Critics, of course, would say the UN already has proved its irrelevance by failing to stop the killing fields in Rwanda or Bosnia.
Even if the US wins a nine-vote majority in the UN Security Council to back military action, and forces Paris to exercise its veto - alone - there will be fence-building to do.
US pundits may ridicule Paris, and question why it even has a permanent Security Council seat, but France’s membership has mostly suited the US very well.
"The UN is a very noble institution. It’s been here over 50 years and it will continue to serve a purpose in the future," is Mr Powell’s response.
The older George Bush spoke recently about the importance of keeping good relations with old allies. "We have differences with European countries, and they’ve got differences with us," he said in a rare public speech late last month, interpreted as a helpful hint to his son.
He emphasised that in his own White House tenure, "I worked on those relationships, and I feel confident when all this calms down, when Iraq lives within the international law, you will see the United States back together as allies and friends with both Germany and France".
Mr Bush noted how after the first Persian Gulf war, US anger with Jordan - which sided with Saddam Hussein - was mixed with understanding over the Arab country’s delicate position.
"I think there’s a message in that for those who today say, ‘How can we ever put things together? How can we ever get talking when you have such acrimony and such bad feeling?’" The answer, he said, is: "You’ve got to reach out to the other person."
The US president himself has stressed recently that "relations with France are going to be very important in the future, just like the relations with Germany". Russia, for its part, has repeatedly stressed its shared interests with the US, even as it has taken the French side in the Security Council. Yuri Fedotov, the deputy foreign minister, criticised the US yesterday for "constantly changing the rules of the game".
But he stressed: "We have too many common interests in the world".
Mr Bush is said to harbour a personal grudge against the German chancellor, Gerhard Schrder.
But Mr Schrder’s election victory last year, on an anti-war, anti-US ticket, has left him with a feeble majority - and his position will weaken further if the war he has tried to stop is a success.