George Bush famously declared the Iraq war over in May 2003 on the deck of the USS Abraham Lincoln, though as it turned out the worst was yet to come.
Barack Obama wisely avoided using the fateful words "mission accomplished" today. But he made as clear as he could that he was drawing a line under the policy of the previous administration. That means the end is finally in sight.
Even with 50,000 US troops due to remain in Iraq after August 2010, there is now a firm deadline for winding up the occupation, consigning to the past what so many regard as a disastrously ill-conceived intervention that brought mayhem, sectarian strife and terror - along with the overthrow of Saddam Hussein.
Obama's announcement finds Iraq in better shape than might have been imagined a year or so ago, when the first substantial benefits of General David Petraeus's troop "surge" were beginning to be felt.
But there is not a policymaker in Washington who does not recognise that these dramatic gains remain fragile. Violence is down from the peak of thousands of Iraqis who were dying every month in 2005 and 2006. Still, the last week alone has seen a rash of bombings and shootings that have left at least 20 dead.
Nouri al-Maliki, the Shia prime minister, has managed to rein in the worst manifestations of sectarianism in the security forces - though only by using highly centralised powers. Al-Qaida and other Sunni extremists have not been eradicated, as over-optimistic US intelligence briefings were suggesting a few months ago. The Shia Badr brigades and the Mahdi army are still able to function. Mosul remains highly volatile.
It is to the new American president's credit that he did not overstate what he could achieve, speaking only of finding "a way forward in Iraq that leaves Iraq to its people and responsibly ends this war". As David Miliband, the foreign secretary, put it in on a visit to Baghdad: "The Obama administration is recognising reality but proceeding in a careful and appropriate way."
Toby Dodge, an Iraq expert at London University's Queen Mary College, said that Obama can look at a largely positive balance sheet. "Over 2007 and 2008 there was a sustained reduction in violence and the rhetoric and anger surrounding the civil war abated. The question is whether it is sustainable."
Voting patterns in January's peaceful provincial elections showed support for nationalist and non-sectarian candidates, though some fear renewed violence around December's national elections. The details of Obama's plan reflect the concerns of his top military commanders on that score.
But another worry, says Dodge, is that the price of Iraq's freedom will turn out to be an authoritarian political system. "Underpinning all this is the fear that all the Americans have done is create another dictator in the making - Maliki, a Putin-like figure. But given where Iraq was two years ago that's not the worst possible outcome. The Americans invaded this country and brought it to civil war. The Americans, under Petraeus, pulled it back from the brink. It is now time that they left the Iraqis to decide where the country goes."
Recent weeks have seen a succession of good news stories from Iraq, including the ceremonial reopening of the national museum, whose looting in 2003 symbolised the abject failure to plan for the post-war period. There has also been reassuringly normal talk of constructing a Baghdad metro system.
Obama's plan will be welcomed across the Arab world. Even neighbouring Syria, once a conduit for foreign jihadis fighting the Americans, now accepts the status quo and has sent its ambassador back to Iraq. The conservative Sunni states such as Saudi Arabia, Egypt and Jordan accept that Iran is a greater regional threat than a new Shia ascendancy in Baghdad.
Even Tehran, hoping for a new, less adversarial start with Washington despite the simmering tensions over its nuclear ambitions, has pulled back from supporting Iraqi Shia groups in recent months. The largely autonomous Kurds, at odds with the Maliki government over land and oil, may be worried about the prospect of an accelerated US pull-out.
Viewed from the region, Obama still looks like a bright new hope, even if expectations of what he can achieve are exaggerated. Bush's war saw US prestige in the Middle East hit an all-time low.
The scandals of Abu Ghraib and Guantanamo Bay tarnished America's claim to be defending freedom. The occupation of Iraq was also accompanied by an open bias in favour of Israel in its conflict with the Palestinians.
Obama's promise to engage with the peace process has been proven by his appointment of the veteran senator and Northern Ireland peacemaker, George Mitchell. Hillary Clinton's first Middle East speech as secretary of state in Egypt on Monday will be closely watched.
Obama's plan won strong official support from Baghdad, even before his speech. "We have faith in our armed forces and our security services to protect the country and consolidate security and stability," said Maliki. "We have no worries for Iraq if American troops pull out. Thank God we have succeeded in ridding ourselves of sectarianism and racism."
