One of Jimmy Carter’s greatest talents is irritating people.

The former president’s deep religious faith and self-righteousness have convinced him he can jawbone any despot into responsible behavior. He once admitted: “Rosalynn (his wife) often says I’m too sympathetic to people who are unsavory, but I have to understand their position.”

But I didn’t get irate like some over Carter’s visit last week with the leader of the militant group Hamas, Khaled Mashal, in Damascus. His mission failed, but it underlined the problems hobbling the Bush administration’s last-ditch try at Middle East peace.

Carter’s problem is not that he’s willing to talk with bad guys, but that he believes every despot can be swayed by dialogue. Not so. Yet his 1994 trip to North Korea – which infuriated the Clinton White House – gave Kim Il Sung a face-saving way to avoid war.

Such a face-saver is needed to help Israel avoid being dragged into a reinvasion of Gaza, which would end future hopes of peace talks.

Right now, Israeli Premier Ehud Olmert is engaged in U.S.-backed dialogue with Palestinian Authority President Mahmoud Abbas that is going nowhere. Abbas is undercut by the fact that Hamas won elections and now controls Gaza.

In recent months, Hamas has been rocketing Israeli towns. Israel has closed the Gaza Strip to all but humanitarian aid – creating a gigantic prison. Such conditions strengthen Palestinian support for Hamas, an Islamist group that won’t recognize Israel’s right to exist.

The only hope to strengthen Abbas’ hand – and turn his public against Hamas – would be to demonstrate progress in peace talks (in which most Palestinians and Israelis have lost faith).

Last Thursday, Abbas visited the White House, where President Bush said he supported a “viable (Palestinian) state that doesn’t look like Swiss cheese.” He meant a state that wouldn’t be chopped up by Israeli settlements and roads.

Indeed, if there is one move that might strengthen Abbas, it would be an Israeli freeze on settlement expansion, as called for publicly by Bush. Yet Israel is expanding existing settlements. Olmert contends that Bush and Secretary of State Condoleezza Rice signed off on such expansion; the White House denies this.

The impasse underlines the slim chance for serious Israeli-Palestinian progress during Bush’s term. Without such progress, Gaza will fester and Hamas’ strength will grow.

One alternative way to tamp down the Hamas threat would be progress on the Israel-Syrian peace track. Syrian President Bashar al-Assad said yesterday that Olmert had offered an Israeli withdrawal from the Golan Heights in return for full peace. Israel’s media confirmed that the Turkish Prime Minister Recep Tayyip Erdogan was carrying messages from Olmert to Assad. And Olmert hinted of movement on the Syrian track.

But Israeli media analysts are dubious that talks with Syria will start before U.S. elections. For one thing, Syria wants U.S. involvement, and the Bush administration wants to isolate the Assad regime. Another wild card comes from new revelations this week about alleged North Korean help to Syria to build a plutonium-based nuclear energy reactor – a site bombed last year by Israeli planes.

So with no progress likely on the Palestinian or Syrian fronts, how to deal with Hamas? The worst option would be a major Israeli invasion and reoccupation of Gaza. Like the invasion of southern Lebanon, this would be a high-casualty venture that wouldn’t eliminate the problem. If Israel left – and the Israeli government would be loath to resume control of the strip – the rockets would be certain to resume.

Israel is already negotiating behind the scenes, via Egypt, for a prisoner exchange and cease-fire with Hamas. So far no success. If achieved, such a cease-fire would be temporary, but might last at least until a new U.S. administration arrived.

This brings us back to the voyage of Carter to Damascus. I’d hoped a slightly zany peacemonger like Carter, not representing the administration, might make a breakthrough on a cease-fire.

Instead, Carter emerged claiming a bigger breakthrough – that Hamas had agreed to live beside Israel. In reality, spokesman Mashal said Hamas would not recognize Israel even after a peace deal, and would demand the right of all Palestinian refugees to return to pre-1948 Israel. This would mean the end of the Jewish state.

The moral of Carter’s visit is this: There is nothing wrong in talking to bad guys, and it might conceivably prove useful.

But such conversations must focus on the possible, avoiding illusions. Let’s hope Egypt can broker the cease-fire Carter failed to achieve.