But, less than 24 hours before today's deadline of 1400 GMT, Madeleine Albright, the American Secretary of State, appeared to be making only the slowest of progress.
And without the assent of the Albanians, it is impossible to get Slobodan Milosevic, the Yugoslav President, where Washington wants him, facing a stark choice between the acceptance of Nato peace keepers or the certainty of allied airstrikes.
There are two big stumbling blocks for the Kosovo Albanians: the plans to disarm the Kosovo Liberation Army, which has led the bloody guerrilla war against Belgrade for the last year; and the absence from the final draft document of any mention of a referendum that would guarantee the independence the Albanians are seeking. Last night General Wesley Clark, Nato's supreme commander in Europe, arrived unexpectedly in Rambouillet, apparently to reassure the Albanians that they would be adequately protected by the alliance even without the KLA, and even if - as seems increasingly possible - a peace keeping force contained a large contingent of Russians, traditional allies of the Serbs. Yesterday Igor Ivanov, the Russian Foreign Minister, raised this very option by declaring that Russian troops could join the force if it was authorised by the United Nations and had the approval of Belgrade.
But Nato's line, reiterated at the alliance's Brussels headquarters yesterday, is that the 28,000-strong force must be Nato-led and unencumbered by any type of "dual key" arrangement which fatally undermined the Western troops supposed to keep the peace in Bosnia before the 1995 accord.
The Serbs, meanwhile, continued their strategy of trying to separate the political and military parts of the deal, and play upon Western divisions over the use of force, growing more obvious as the final negotiating showdown approaches. Speaking before another session with Mrs Albright yesterday, Milan Milutinovic, the Serbian President, said Belgrade might be ready to talk about foreign troops once a political agreement granting autonomy but not independence for Kosovo had been reached.
That would be the ultimate quandary for the West: what to do if Mr Milosevic signed up to the political agreement and put foward suggestions for a peacekeeping force, less directly controlled by Nato? Almost certainly Italy, and perhaps France, would oppose any airstrikes.
As the frantic diplomacy continued in France, it was fighting as usual in the southern Balkans. Yugoslav armour and KLA fighters clashed for more than three hours near Vucitrn, north of Pristina, sending hundreds of civilians fleeing for their lives.
And, in a sign that hostilities may be about to intensify, it was reported in Kosovo that the KLA had chosen Suleiman Selimi, 29, a radical hardliner, as its supreme commander.
What will Happen Next?
If both Serbs and ethnic Albanians accept the big powers' peace plan
28,000 NATO troops would be deployed in Kosovo, and a new constitution would be introduced amid preparations for elections in nine months. Some sanctions would be lifted on Yugoslavia. Kosovo would receive international aid.
If the Albanians accept but the Serbs do not
THIS WOULD open the way to Nato air strikes against Yugoslav targets, and guarantee Nato protection for Kosovo.
If the Serbs accept, but the Albanians do not
THE WESTERN nightmare. The Kosovars would be told they have to face the Yugoslav army alone, with the near certainty of massive bloodshed.
If both the Serbs and the Albanians refuse
RAMBOUILLET WOULD have been a complete failure, and the West would restart the search for a solution from scratch.
If the Albanians accept, and the Serbs say 'Yes, but...'
THE TRICKIEST of all for the West. Suppose Mr Milosevic agrees to the political side, but says he wants UN, not Nato peacekeepers? The West says the package is all-or-nothing. But can we really bomb Belgrade over a dispute about who keeps the peace?