Not only did it wrongfoot the Al-Qaeda terrorists waiting in the wings to spoil the trailed 'big day' of 30 June with unwanted fireworks, but it sent a message to all the critics of the Iraq situation: this was not an 'occupation' we want to continue for one day more than necessary and we are anxious to leave as soon as possible. Another nice touch was that the Iraqis announced Bremer's early departure themselves. Even the low-key ceremony in one of Saddam's palaces was a masterstroke of modesty, looking more like an employee of the month celebration than an historic occasion.
It was also a spin trick of Alastair Campbell proportions. Any corporate PRO would have been proud if they had outfoxed journalists and the markets by bringing forward some expected announcement and hijacking the news agenda in such a way. But hold on. Has Tony Blair really got Iraq off his hands? British troops are still there, and the question of whether to send 3,000 extra troops will continue to cause anxiety.
There is Lord Butler's report on intelligence in Iraq, which is coming very soon and causing much anxiety in Downing Street. Aides know that the former cabinet secretary will not want to be tarnished by the same 'whitewash' jibes as Lord Hutton, and they expect some uncomfortable findings this time.
Then there are November's US presidential elections. Blair is conscious that if his war ally George Bush is defeated, there will have been yet another casualty of Iraq. Maybe even he will be next, the PM must wonder.
And a Democrat White House under John Kerry could be a much cooler and unwelcome place because of his anti-war stance. Doing things early also seems to be the order of the day in Number 10, hence Blair called 'snap' by-elections in Birmingham and Leicester, which are likely to bring further blows, to get them over with before the summer break.
Maybe the PM might even surprise us all by calling a general election when he returns in the autumn. With mortgage costs going up, by next summer, when we all expect Blair to call it, voters could be starting to feel the pinch in their pockets. But I wouldn't bet on Blair giving an early handover to Gordon Brown.
David Cracknell is political editor at The Sunday Times
Charlie Whelan is on holiday.