Israelis are fed up with what they see as a failed Gaza policy. Hamas’s attacks keep spoiling the peace efforts of moderate President Mahmoud Abbas, and Israel’s retaliatory strikes in Gaza have backfired. Public opinion was hit hard earlier this month when Israeli raids killed more than 50 Palestinian civilians. “Hamas is not going to disappear,” says Shlomo Brom, a former Israeli military chief of strategic planning who advocates indirect negotiations. Damascus-based Hamas leader Khaled Meshaal told NEWSWEEK last year that his organization was open to direct talks, as long as there were no preconditions.

High-profile meetings are all but unthinkable. Israeli Prime Minister Ehud Olmert, his popularity hovering in the single digits, doesn’t dare alienate the right-wing parties that are keeping him in power. And which Hamas should Israel deal with? Since seizing control in Gaza last June, the organization has split into a pack of independent power bases. “When you talk to Hamas, you don’t have one address,” says a former Israeli intelligence operative who has held direct talks with the Islamists in the past and who asked for anonymity on such a delicate topic. “You have to deal with several figures in order to achieve approval for anything.”

That hasn’t kept Israel from quietly holding behind-the-scenes talks—especially with jailed Hamas representatives. Last summer Ofer Dekel, a former Shin Bet intelligence officer assigned to negotiate the release of captured Israeli soldier Gilad Shalit, met with senior Hamas officials at Israel’s Hadarim prison. Lawyers for Shalit’s father, Noam, are also seeking a sit-down with Hamas in Gaza. So far the Israeli government has withheld travel permission. But one thing is sure: ignoring Hamas hasn’t made it go away.