ne of the remarkable aspects of the Israeli-Palestinian struggle is that after so many failed attempts at peace, new initiatives can still rouse hopes. They may not be high for the success of the "road map," and every politician on every side has taken care to raise the caution flags. Indeed, everything being witnessed these days — the summit meetings, the cease-fires, the pullbacks — has been done before. For Hamas and Islamic Jihad, a three-month cease-fire is a tactic, not a conversion. The Israelis are still working on their separation wall, and are a long way from actually uprooting a real settlement.

But after all the caveats and doubts have been registered, there is enough to justify hope. Yesterday's meeting between Mahmoud Abbas and Ariel Sharon, the Palestinian and Israeli prime ministers, was businesslike, apparently even warm, and productive. President George W. Bush and his partners in the quartet that drew the road map — the United Nations, the European Union and Russia — must now not relent in their pressure on both sides. For this they must be flexible, evenhanded, patient and very tough.

What sustains hope is not so much the formal actions as how they are being achieved. The fact that Marwan Barghouti, the popular West Bank leader who has been in an Israeli prison for more than a year, was allowed to mediate with the militants is an encouraging sign that the Israeli government knows when to relent. Mr. Barghouti, a leader of Fatah, the group of Prime Minister Abbas, has the credibility among Palestinians that Mr. Abbas lacks. With Muhammad Dahlan, the security minister, the Palestinians finally have a leadership team that might find traction among their own, as well as with the Israelis and Americans.

That is critical. After so many months of unrelenting violence and so many broken deals, a major challenge for the leaders of either side is to sell any concession, any accommodation, to their own constituents. On the Israeli side, the time is past when most of the public believed that a peace settlement was the key to security. First and foremost, the Israelis want their government to fight terror, and if attacks resume, Mr. Sharon will oblige.

Yet he has demonstrated in Gaza and in Bethlehem that he is prepared to make life easier for the Palestinians, and he is talking to Palestinian leaders. That is a long way from the really tough steps that lie ahead on the road map, like uprooting a full-fledged Jewish settlement, but at least it gives the Palestinians the sense that their new leaders are getting them some concrete relief.

So yes, these are all very small steps, and yes, we have been here before. But at this early stage, small steps go a long way. President Bush must keep pushing for the next step, and the next.