Change we can believe in?
I've been thinking about something an American pundit said to me when we were discussing Barack Obama's election last November. "Just because we've changed presidents," she said, "doesn't mean that the rest of the world has changed as well."
I wonder if Mr Obama is thinking something similar as he ponders the results of his travels. Because he may be feeling that he doesn't have a great deal to show for all his glad-handing and speechifying.
I don't want to sound mean-spirited, so let's deal with the positives first. Yes, he was well received - even rapturously received - pretty much wherever he went. He spoke well, he seemed to be listening as well - and he said many of the things his hosts hoped to hear from him. And, if it matters, the First Lady was a great success too.
From the London summit to the NATO summit, from the Prague speech on nuclear disarmament to the speech to the Turkish parliament, the verdict of the punditocracy was that he didn't put a foot wrong.
But did his fellow world leaders in London accept his idea for a globally-agreed fiscal stimulus package? No. Did European leaders in NATO agree to send thousands more troops to Afghanistan to join the US in its counter-insurgency and counter-terrorism operations? Only in a very limited, and temporary, way.
And as for that briefest of touch-downs in Iraq, he arrived just a day after a co-ordinated series of bombings in Baghdad that cost nearly 40 lives. The suspicion is that restive Sunni militiamen are flexing their muscles as the (Shia) Prime Minister Nouri al-Maliki tries to rein them in.
Mr Obama would like us to think that Iraq is no longer a major problem. He'd much rather we focussed on Afghanistan, Pakistan, and Iran. But I fear that Iraq is in fact still a major problem, or at least that it has the potential to be one. (Yesterday was the sixth anniversary of the fall of Baghdad to US forces, and it was marked by a huge demonstration calling for the US to get out now.)
It has long been acknowledged by military strategists that withdrawals are uniquely risky undertakings. Soldiers are never so vulnerable as when they are packing their bags and preparing to fly home. What's more, they inevitably leave a hole, which others want to fill for them after they have gone.
Here's what I'd be worrying about if I were contingency planning. First, the Sunni fighters of the Awakening Councils, whose anti-al Qaeda operations were a crucial element in reducing the levels of violence. Can Mr Maliki be persuaded to treat them with a degree of respect and understanding which until now he has seemed unprepared to show?
Second, the oil-rich city of Kirkuk, and the flashpoint city of Mosul. Both are tinder-boxes, and both have the potential to erupt at any time. The top US commander in Iraq, General Ray Odierno, is quoted in The Times today as saying that trouble in Kirkuk and/or Mosul could result in US combat troops staying in Iraq beyond the Obama-imposed deadline of 30 June next year.
(By the way, the number of US military deaths in Iraq last month was nine, the first time it has been in single figures since the invasion six years ago. The total number of US military deaths is put at 4,266.)
[UPDATE: Five American soldiers and two members of the Iraqi security forces were killed in a massive suicide truck bombing on Friday near the headquarters of the Iraqi national police in the northern city of Mosul, according to a US military spokesman.]
Don't forget: President Obama is now committed to a major escalation of US military involvement in Afghanistan. The last thing he wants is for things to get worse again in Iraq - but he can't be sure that won't happen.
And my sense is that if things do get worse, he won't get much help from US allies, however much they may have applauded his speeches over the past week. The prevailing view seems to be: "You lot got us into this mess, so you can get us out again." Not pretty, maybe, but hard times breed hard politics.