TEL AVIV, Israel — People don't ordinarily think of Ariel Sharon as a mama's boy. But he was. And he had some mother, too. Even among the flinty Zionist farmers of the 1920s, she stood out as a hard case, a woman of epic quarrels who carried a grudge and slept with an ax under her bed.

Sharon's mom lived to a ripe old age, and she never stopped exerting an influence over her son. Last month in Paris, he offered a peek at their relationship to a French-Jewish audience.

He recalled negotiating in Cairo back in the 1970s, as a senior member of Menachem Begin's government. By day he haggled with the Egyptians over the terms of peace. By night he called his mother. She'd give him a detailed report of her activities on the farm she still worked well into her 80s, then end with a maternal admonition about Arabs: "Never trust them."

Sharon never has, and this mistrust is at the heart of his decision to unilaterally withdraw Israeli settlers and troops from the Gaza Strip. It is also the key to understanding what he will do next.

For the prime minister of a famously garrulous nation, Ariel Sharon is a man of few words. He has been justly criticized for failing to explain to Israeli voters (or even members of his own Likud Party) his decision to leave Gaza. And he has been intentionally opaque about his plans for what will come next.

Last Friday, though, on the eve of the Gaza withdrawal, in an interview with the daily newspaper Yediot Aharonot, Sharon gave a strikingly succinct explanation of his diplomacy. "I've reached a deal with the Americans," he said. "I prefer a deal with the Americans to a deal with the Arabs."

American presidents since 1967 have been trying to get Israel to make a deal that includes leaving territories it occupied in the Six-Day War. Until now, not one of them has been successful. But George W. Bush has pulled it off.

This diplomatic success was possible only because Bush won Ariel Sharon's trust. Previous administrations tried to bribe or pressure Israel into making territorial concessions. The president used different tools — common sense and credibility.

As a master politician, Bush realized that there were political limits on what Sharon could do. Neither Sharon nor any conceivable Israeli prime minister would ever evict the hundreds of thousands of Israelis who now live in East Jerusalem and the major settlement blocs of the West Bank. Asking for that would be an automatic deal-breaker. Same for the Palestinian demand that millions of Arab refugees and their descendants be "returned" to Israel. And Israel would never relinquish its option to respond militarily to armed aggression.

Bush acknowledged these Israeli truths in an official letter he sent to Sharon in April 2004. In exchange for that recognition, however, the president asked for — and got — Sharon's agreement to do what he could do. Evacuating Gaza was one of those things.

The American vision for Middle East peace sees exit from Gaza as a first step. Next comes an Israeli withdrawal from those settlements in the West Bank that aren't already de facto parts of Israel, and then the creation of an independent Palestinian state.

These concessions are wildly unpopular with people who once voted for Sharon. Many of them spent the day in Gaza loudly denouncing the prime minister and his policies. Sharon's chief Likud Party rival, Benjamin Netanyahu, is currently trying to capitalize on this by warning that abandoned territories will inevitably turn into bases of Islamic terror.

Netanyahu offers Gaza as Exhibit A.

Netanyahu may well be right, and Sharon knows it. But the deal Sharon cut with Bush takes that into account. It comes with an escape clause. Further Israeli concessions are predicated on the Palestinian Authority — led by President Mahmoud Abbas — taking control and disarming the Fatah, Islamic Jihad and Hamas gunmen.

If Gaza under Abbas becomes a neighborly, prosperous Mediterranean Singapore, fine; in that case, following the U.S. plan to an independent Palestinian state will make sense to Israelis, even to many Likud voters.

But if Abbas and his colleagues won't (or can't) pacify Gaza, Bush has made it clear the process stops. A cessation of terrorism is the U.S. precondition for further Israeli concessions.

Of course, other American presidents have made similar assurances. But Bush's Middle East policies — from the toppling of Saddam Hussein to the fight against Islamic terrorism — have given him special credibility in Sharon's Jerusalem.

With Bush in the White House, an ax under his bed and his mother on his mind, Sharon is ready to give peace a chance.

Zev Chafets is writing a book about Christian evangelicals, American Jews and Israel. He wrote this commentary for The New York Times.