Why the new interest?

Because the US Secretary of State, Condoleezza Rice, was in Jerusalem last week for a two-hour, three-way summit with the Palestinian president Mahmoud Abbas and the Israeli prime minister Ehud Olmert, and promised to come back "soon".

What were the results?

Minimal. There was no press conference and only the blandest of statements afterwards. The most that can be said right now is, firstly, the dialogue will continue . . . and under Rice's auspices . . . and secondly, by making clear the US wants Abbas to stay in play, Rice headed off any possible attempt by Olmert to carry out his halfthreat to end contacts with the Palestinian president because he signed a coalition deal with Hamas.

What's Condi up to?

Good question. Whatever you think about the underlying strategic goals of a battered US administration . . . from fomenting a multinational Sunni coalition against a perceived Shia threat, to extricating itself from Iraq without national humiliation . . . it is obviously trying to shore up support from the friendlier Arab regimes. And to do that, Rice needs to show some sign of trying for a solution to the Israeli-Palestinian conflict.

She still hasn't abandoned the threeyear-old Road Map but she has tentatively started to hold out the prospect of eventual discussion on what the end of the process might be, the 'endgame' . . . in other words, what a lasting two-state solution might look like. That's what she means when she talks of a "political horizon" and says "the Palestinian peoplef could benefit from knowing that there is in fact a destination and that the Israelis and Palestinians are prepared to talk about that destination".

What isn't clear is whether Rice will consider the administration's goals fulfilled if she is seen to be trying, or whether she really wants, against all the odds, to pull off some kind of breakthrough before Bush steps down. And, if it's the latter, does she have the real backing of the US president and the most hawkish elements outside the State Department, or are they content to see her try and fail?

So what are her chances of making this amount to something?

On the face of it, they could hardly look worse, given the weak internal positions of both Abbas and Olmert. Abbas has long made clear his desire for a two-state peace.

But even if Olmert, who until the Lebanon war was in favour of unilateral withdrawal from parts of the occupied West Bank, wanted to negotiate a lasting solution, he would be in deep trouble with the right for even contemplating dividing Jerusalem or doing the kind of deal on borders that Abbas could possibly accept. Which is one reason why he has been resisting any talk of 'endgame' . . . or at least one beyond some kind of 'interim' deal on borders, which Abbas has made clear he won't accept.

What's more, he has the ready-made excuse that, even under the recent Mecca deal establishing a unified Palestinian government, the legislature, the premiership and nine of the cabinet's seats will be in the hands of Hamas, which doesn't even recognise Israel.

Isn't that a deal-breaker?

Well, not necessarily. In theory at least, Abbas, as head of the PLO, could conduct whatever negotiations he wanted and bring the outcome back to a referendum of the Palestinian people. While expressing deep scepticism that such talks would get anywhere, Hamas have indicated they wouldn't stop him doing that. But the role of Hamas is certainly a complication.

The US and Israel show every sign of refusing to lift their boycott of the PA if and when the Saudi-brokered unity government takes office. And even if the US were suddenly to exert real pressure on Israel . . . a very big if indeed . . . to talk 'endgame' with Abbas they would hardly be ready to contemplate handing over territory to a PA in which Hamas still had the upper hand.

So why is Dr Rice talking about 'horizons'?

Partly of course, this is all about . . . very belatedly . . . trying to give Abbas some political cards in his competition with Hamas for the hearts and minds of the Palestinian people.

While most Palestinians are mightily relieved that the deal was struck at Mecca, because it offers respite from the bloody in-fighting between the factions, many fear that the coalition might not last too many months.

Elections, already threatened by Abbas, would then be a possibility . . . though it's hard to see how they could happen without at least tacit acceptance by Hamas. And Abbas will need something to offer the electorate.

Beyond that, the few hardcore optimists believe that Bush might just be seeking one positive element to counter-balance the negatives in his legacy to the region.

Is there a chance Bush could succeed where Clinton failed?

There's a paradox here. First, we are nowhere near even the Camp David stage in 2000 or, more relevantly, the later talks at Taba when the parties drew closer. Bush doesn't have Clinton's vision. Olmert is not Ehud Barak, the Israeli PM at Camp David.

And Abbas doesn't have Yasser Arafat's capacity to sell a deal. And all those failed.

Moreover, because of what Ariel Sharon used to call "facts on the ground", the sheer physical changes involved in even the minimum deal that Abbas could possibly accept . . . the destruction of Jewish West Bank settlements, the unravelling of road networks, the dismantling or wholesale rererouting of the separation barrier . . . are far greater now than seven years ago.

On the other hand, the polls suggest it's truer now than it was then that a majority of Palestinians and Israelis roughly agree on the kind of settlement . . . based on 1967 borders . . . they would accept.

Secondly, a logical lesson of last summer's Lebanon war for Olmert is that seeking to eliminate your enemies . . .

whether Hizbollah or Hamas . . . by military means may not always work, and an Israeli PM, badly in need of an agenda, might never have a chance of a better deal than with Abbas.

So there are grounds for optimism, then?

Hardly. That really would be flying in the face of the history of the past 40 years.