An end to violence. Concrete steps to eliminate friction. A joint effort to prevent a recurrence.
It all sounded most impressive when an exhausted President Clinton, apparently salvaging victory from the jaws of defeat at the bitter Sharm al-Sheikh Summit, announced yesterday morning that those peace partners-turned-enemies - the Israeli Prime Minister, Mr Ehud Barak, and the Palestinian President, Mr Yasser Arafat - had agreed to put a halt to Israeli-Palestinian violence.
But back in the West Bank and Gaza Strip, a short flight from Sharm to the combat zone where more than 100 Palestinians have been killed in the past two-and-a-half weeks, there wasn't even a pause in the fighting to digest the supposedly good news.
A truce? A withdrawal of forces? Not at Rafiah, at the foot of the Gaza Strip, where gunfire raged and a Palestinian policeman was killed.
Not in Bethlehem, where thousands of Palestinians marched in the funeral procession of a teenage Palestinian, Muayed Dar wish, killed on Monday.
Chanting "No to Sharm al-Sheikh, yes to armed struggle", groups of youths then broke away from the procession and headed for Rachel's Tomb, a well-fortified religious site that marks the friction point between Israeli- and Palestinian-held territory, and threw stones and petrol bombs at the Israeli soldiers, drawing rubber bullets in reply.
Not in the Nablus area, where two settlers were arrested by Israeli police after a Palestinian man was shot dead and three others were injured at the settlement of Itamar. The settlers claimed they fired in self-defence, having been attacked with axes and knives; the Palestinians claimed they were picking olives in the fields adjoining the settlement, and that the shooting was unprovoked.
And not in Gilo, a southern Jerusalem neighbourhood, where an Israeli Border Policeman was critically wounded by gunfire from the town of Beit Jalla, across the valley in Palestinian territory. Palestinian opposition groups - Hamas, and rejectionist factions of Mr Arafat's PLO - are deriding the Sharm understandings, insisting they do not feel bound by them, and even describing them as a "betrayal" of their dead.
More ominously, some of Mr Arafat's own ostensible loyalists, are rejecting the agreements too. A Fatah leaflet in Gaza called for continued protests against soldiers and settlers today. And Mr Marwan Barghouti, who heads the "Tanzim" paramilitary force in the West Bank, and who is supposed to take orders from Mr Arafat, declared: "This peaceful intifada will continue until sovereignty and independence."
The Israeli government says it hopes the violence will ebb in the next day or two. And if it doesn't? "Then I don't know," said Mr Avraham Burg, the Speaker of the Knesset, from Mr Barak's Labour Party.
If it doesn't, then the death toll will rise, and Mr Arafat will head off to an Arab summit this weekend to furious criticism from hardline Arab countries such as Iraq and Syria, which oppose normalisation with Israel and which will see yesterday's Sharm "success" as a sell-out.
And President Mubarak of Egypt, and King Abdullah of Jordan, key players in achieving yesterday's understandings, will be hard-pressed to defend them, and will have their own peace treaties with Israel subjected to angry scrutiny.
The spiritual leader of the Islamic militant Hamas group said yesterday the agreement reached at Sharm al-Sheikh was not binding on his movement.