At the White House today President Clinton will host the first negotiations between an Israeli Prime Minister and a top Syrian leader. The meeting has aroused intense anticipation that two of the Middle East's most uncomfortable neighbours are finally about to resolve their differences.
In the dream scenario, Mr Clinton watches happily as Israel's Prime Minister, Mr Ehud Barak, and the Syrian Foreign Minister, Mr Farouq al-Sharaa, shake hands warmly and smile for the massed cameras. After talks today and tomorrow they all get together again, to announce the formal cessation of the state of war between Israel and Syria.
And within a few months, following non-stop negotiations - perhaps in Jordan, perhaps in the US - Mr Barak and, this time, Syria's President Hafez al-Assad affix their signatures to a full peace treaty. Mr Assad is hailed in his country as the greatest leader Syria has ever known, and the path to succession of his son, Bashar, is smoothed. In Israel the treaty, though it involves painful territorial compromise, is overwhelmingly endorsed in parliament and, in a nation-wide referendum, by the public.
If this sounds absurdly optimistic, it is worth remembering that both Mr Barak and Mr al-Sharaa have in recent days expressed the hope of reaching a full treaty "within months," and that officials in Damascus assert that "80 per cent" of the deal is already done.
In the nightmare scenario, however, the talks quickly run into trouble over any one of innumerable potential obstacles.
While Israel is evidently ready to agree in principle to withdraw from the Golan Heights, the strategic ridge whose fate has stood at the heart of the Israeli-Syrian dispute since Israel captured it in 1967, the sides may well differ, for example, on precisely where the new border should run. The Syrians may insist that the line be drawn to give them access to the Sea of Galilee; Israel would likely be adamant that the border run to the east of the sea.
Similarly, there is plenty of room for argument over the timetable for withdrawal.
Mr Assad, not in the best of health, wants a swift Israeli pullout, with the Golan back in Syrian hands in his lifetime. Mr Barak wants a long trial period, to prove Syrian good intentions. There could be disputes about water resources: much of Israel's water reaches it through the Golan.
The terms of normalisation could be hard to pin down. Israel wants much warmer diplomatic, trade and tourism relations than Syria would ideally countenance.
And Lebanon could present problems, too. Israel will want the Syrian army to help keep the Israel-Lebanon border quiet while the negotiations are in progress, but Syria may want to reserve such co-operation for a later stage.
Mr Barak's aides have this week been citing the Jordanian precedent to justify their optimism: Yitzhak Rabin met King Hussein publicly for the first time in July 1994 in Washington; by that October the two men were meeting again, on their agreed border, to sign their peace treaty.
If things go that smoothly with Mr Assad, they say, Israel could have peace on all its borders by next summer, with much of the rest of the Arab world clamouring to establish relations.
But King Hussein, of course, had been meeting Israel's leaders privately for decades, and was a secret friend. Mr Assad is, today at least, regarded in Israel as an enemy. He and Mr Barak have their work cut out to persuade the Israeli public to back a Golan-for-peace deal, always assuming that he and Mr Barak can reconcile their differences and reach that deal in the first place.