Israel’s Foreign Minister, Avigdor Lieberman, has made his reputation telling what he imagines to be hard truths that others shrink from. He says that he sees the world “bli ashlayot”—without illusions. In 2001, he said that if Egypt stationed troops in the Sinai, Israel should respond “strongly,” by, say, bombing the Aswan Dam, on the Nile. He has said that Israeli Arabs who don’t swear loyalty to the state should be stripped of citizenship. He has even argued that Israel should negotiate with the Palestinian Authority’s Mahmoud Abbas on the basis of a (demographically agreeable) land swap, whereby Israel would annex large West Bank settlement blocs while handing over to the Palestinians three hundred thousand third-generation, Hebrew-speaking Arab citizens in towns near the pre-1967 borders.

Since the beginning of the latest Gaza operation, Lieberman, unsurprisingly, has done to Prime Minister Benjamin Netanyahu what Netanyahu did to his predecessor, Ehud Olmert, in 2009: outflank him on the right by insisting that no ceasefire be considered until Hamas is vanquished. The current ceasefire is still provisional, and Lieberman has declared that Israel will not coöperate with any war-crimes investigation by the United Nations Human Rights Council.

It was surprising, then, that when Lieberman testified before the Knesset Foreign Affairs and Defense Committee last week, he suggested that Israel and the Palestinian Authority might consider turning control of Gaza over to a United Nations mandate. “Suppose Hamas is defeated,” he said. “What happens after the operation ends?” He went on,

A U.N. mandate is not only part of the history of the land of Israel, we also saw it … in the cases of East Timor and Kosovo. We saw U.N. mandates working, and they worked not badly. And, therefore, here, too, we need to consider returning control over Gaza to the U.N. I certainly don’t rule out this option.

Lieberman may have been engaging in a public thought experiment—evidently, he allows himself many of these. But, in this case, his thinking is unusually pragmatic; the Obama Administration might reinforce his notion with a clearer policy along the same lines before he reverts to form. Any Palestinian administration, and all Gazans, want economic rehabilitation; that means open border crossings, reintegration with the West Bank economy, a port, and an airport. All Israelis want to see Gaza, if not demilitarized, then at least closely monitored, with Hamas prohibited from using ports of entry as a means to spirit in sophisticated weapons—such as missiles that could again cause large-scale flight cancellations to Israel’s airport—or to import construction materials to rebuild its tunnel network. But Israelis can no more trust the Palestinian Authority alone to restrict the inflow of weapons than Palestinians can trust Israelis to facilitate Gaza’s commercial development. There is only one way to advance both urgent purposes, and that is through the presence of an international force on the ground—a force that both sides can trust without having to trust each other. If the current negotiations in Cairo are going nowhere, the internationalization of Gaza’s administration may be the only way to advance them.

Lieberman’s notion of a U.N. mandate was pounced on, of all people, by members of the Knesset peace camp. The man with no illusions was presenting an idea “belonging to another world,” the Labor member Nachman Shai scoffed; it was meant “to sabotage the two-state solution.” In reality, Lieberman’s suggestion presupposes a high degree of coöperation with the Palestinian Authority. And its political logic, however imaginative, proceeds from a solid foundation.

First, Lieberman is right to imply that the war should not leave all parties back where they started, waiting for the next round of violence. Second—this Lieberman implies, but would not admit—the future isn’t solely Israel’s to determine. Israelis are awakening to the fact that a reoccupation of Gaza is virtually impossible; the price in civilian lives would be too high for Israel’s democratic trading partners, and the West Bank and Jordanian street, to tolerate. Hamas, for its part, cannot shape events as it pleases, either. Hamas may be impossible to defeat, but it can be cornered. Gaza’s only crossing to Egypt, Rafah, is controlled by President Abdel Fattah el-Sisi, who regards Hamas as a branch of the despised Muslim Brotherhood, and Sisi wants to regain control of a Sinai that is increasingly threatened by Islamist insurgents. All the other crossings are controlled by Israel, and Gaza’s port is blockaded by the Israeli Navy. As for the funding that will be required for Gaza’s economic development, including money to pay civil servants, most of it is expected to come from Qatar, an ally of the United States; Hamas’s leader, Khaled Meshal, is taking refuge in Qatar, which just bought eleven billion dollars’ worth of American attack helicopters and air-defense systems. Hamas’s most important diplomatic support comes from Turkey, a member of NATO.

This is the kind of stalemate that U.N. peacekeeping was designed for. When I spoke to Ambassador Álvaro de Soto, the former U.N. Special Coördinator for the Middle East Peace Process, who designed the peacekeeping arrangements in Cyprus between 1999 and 2004, he suggested reviving the terms worked out by James Wolfensohn, the president of the World Bank, when Israel withdrew its forces from Gaza in 2005. (After Hamas unexpectedly won a majority in the Palestinian parliament the following year, Israel never fully implemented those terms.)

“Wolfensohn sensibly understood that there could be no restarting of the Gaza economy without freedom of movement,” de Soto said. “So he proceeded to draw up modalities for that to occur—particularly the Rafah crossing into Egypt. European monitors, trusted by Israel, would be stationed there, and there would be a permanent feed, where Israelis would watch what was going on. These monitors should now be based inside Gaza. One could easily imagine NATO troops taking their place today, acting under a mandate of the U.N. Security Council. In principle, the same arrangements could be worked out for the Gaza port, and even for an airport.”

Under this arrangement, de Soto believes, the Palestinian Authority could reëstablish administration of Gaza, including a police force that incorporates elements that have answered to Hamas. The area along the Israeli border, which contains Gaza’s finest agricultural land, and under which any new tunnels would be dug, could be patrolled exclusively by these international forces. As it happens, Abbas already agreed to an arrangement quite like this for Israel's Jordan River crossings, during his 2008 negotiations with Olmert for a comprehensive two-state deal.

But just as Netanyahu spiked that progress, abandoning most of the principles to which Olmert had agreed, there is no guarantee that he will want a U.N. force anywhere in the region—or that ministers like Lieberman would actually provide support. On the Palestinian side, the great problem that de Soto foresees is the fragmentation of insurgent forces. All Palestinian factions are at the table in Cairo at the moment, but who knows whether various underground groups such as Islamic Jihad would remain under anyone’s control? “The basic rule under which international forces are deployed is that the consent of all relevant parties must be obtained,” de Soto said.

Consent will come only if international pressure is brought to bear. Each side has allies who want this horrible conflict to end. Hamas may hate the idea of European troops in Gaza as much as Israel hates the idea of an expanded U.N. presence there. But the hard truth, as Lieberman testified, is that there are worse things.