The Middle East is supposed to be a place of crises and an endless source of transatlantic tension. But the lecturing of Washington is coming to an end, as there is slow but steady progress on a settlement between Israel and the Palestinians. The Bush Administration, including the First Lady, Laura Bush, has been engaged in the region; and the past four months suggest that, on a number of fronts, quiet progress is being made. And, as Jack Straw begins a visit to Israel and the Palestinian territories, he will find that for once there is a hint of optimism in the air.

The issue that has dominated all politics in the region is the impending Israeli withdrawal from Gaza in August. Outsiders, including many neighbouring Arab states, underestimate the importance of this courageous and fundamental shift in Israeli political and strategic thinking — a shift that has convulsed Israeli society and is a severe test of the stamina of Ariel Sharon, the Prime Minister.

His Government’s softly-softly approach has proved astute: by offering the 8,000 settlers generous alternative accommodation on the coast in southern Israel, by instructing the Army to handle the operation with tact and by appealing to public opinion across the political spectrum for support, Mr Sharon has persuaded all but die-hard settlers to accept the plan. He has also faced down the challenge from Binyamin Netanyahu and the right of his Likud party and convinced the Palestinian leadership to negotiate an orderly departure.

Mahmoud Abbas, the Palestinian President, is eager to avoid any incident that could stall the withdrawal. The Palestinian Authority is to recruit 4,500 police to prevent attacks on settlers and looting, but the move will be a stern test of a body that has not distinguished itself in the past. For Mr Abbas, enforcing calm may not prove easy. Hamas and Islamic Jihad are determined to make the pull-out as bloody as possible to bolster their own credentials by claiming credit for forcing the settlers to leave.

Hamas is clearly hoping to capitalise on its growing influence among Palestinians. Since agreeing to take part in the coming elections, it has seen its popularity rise steadily, and may well benefit from Mr Abbas’s decision to postpone the vote on the grounds that preparations have not been completed. Indeed, the Palestinian leader, 70 and recovering from heart surgery, is under pressure from all sides. His gamble that Hamas militancy could be defused by drawing the party into the political process has yet to pay off: the February truce with Israel has so far survived, but the truce has always been uneasy.

Israel is suspicious of this tactic of dialogue with extremists and accuses Mr Abbas of failing to crack down — although many Israelis would admit, privately, that Hamas has posed less of a threat since the assassination of its theological leaders. Significantly, Israel has made only a token objection to Mr Straw’s admission that British diplomats have met two elected Hamas officials.

To his credit, Mr Bush has remained as firm as he has been fair in holding Mr Sharon to the timetable. James Wolfensohn, his special envoy, yesterday began talks on the pull-out with cautious confidence. If this mood holds, those who want to achieve progress could yet prevail over the many saboteurs waiting in the wings.