By Andrew Marr
BBC News political editor
In the end, there was probably only one word that really mattered at the rain-swept Blair-Bush Washington summit: that word was "capital".
Blair and Bush met alone for two hours during the summit
The immensely powerful, unconstrained re-elected US President promised over the next four years to "spend the capital of the United States" trying to create a free and democratic Palestinian state.
If he means it, that is a formidable promise.
But it depends on the Palestinian elections producing a new leadership that is committed to the "road map" solution of two states, Israel and Palestine, and is not dominated by the more extreme groups now jockeying for position in the post-Arafat Palestine; and is utterly committed to extirpating terrorism.
Blair and Bush have agreed to push all the help they can to securing successful Palestinian elections, with the Israelis standing back, and international assistance with monitoring and peacekeeping.
Then, the two men agreed, the limited Israeli pull-out from Gaza and from some West Bank settlements had to be made fully effective. It was essential not to leave behind anarchy or chaos.
President Bush told Tony Blair privately he believed Israel's Ariel Sharon would go far further if that happened, creating the tantalising possibility of a final settlement to one of the world's most dangerous conflicts.
But was this mere summit rhetoric? Is there any, faint, reason for hope this time, after so many dashed hopes, bloody failures and broken deals over past decades?
Mr Blair and his officials hope the coincidence of Yasser Arafat's death and President Bush's re-election, making him look forward to his eventual legacy, gives momentum and movement at last.
Mr Bush's "capital", after all, is immense.
But just as striking was the way both leaders emphasised their central mission - nothing less than the spreading of democracy around the trouble spots and most dangerous regions of the world.
Whether or not this is a doctrine which has been created retrospectively to account for the Iraq war, both seemed to be using near-identical language.
What appears to be emerging from this unusually private summit - the two men were together without anyone else for two hours, and spent several more with just a small team of close advisers - could be called the doctrine of the "new interventionism".
Bush and Blair hope the post-Arafat leadership will stamp out terror
No longer is it acceptable to deal with dictators or hardline regimes, so long as they don't directly threaten the West: in future they have to be confronted and democracy has to be spread by any means possible.
It is a strange marriage between the old internationalist instincts of part of the liberal left and the so-called neo-conservatives of George Bush's America.
This is, quite clearly, a restless, hugely ambitious and no doubt at times perilous world view.
But listening to the self-certain words and observing the body language it was quite clear - both men mean this.