Could Bibi Netanyahu and Barack Obama share the 2014 Nobel Peace Prize? The thought sounds ludicrous on its face, I know. The two do not like each other and have radically different worldviews. But as much as they keep trying to get away from each other, the cunning of history keeps throwing them back together, intertwining their fates. That will be particularly true in the next six months when the U.S.-led negotiations to defuse Iran’s nuclear bomb-making capabilities and the U.S.-led negotiations to reach a final peace between Israelis and Palestinians both come to a head at the same time. If these two leaders were to approach these two negotiations with a reasonably shared vision (and push each other), they could play a huge role in remaking the Middle East for the better, and — with John Kerry — deserve the Nobel Prize, an Emmy, an Oscar and the Pritzker Architecture Prize.

Let’s start with the Iran talks. After his initial and, I believe, wrongheaded outburst against the U.S.-led deal to freeze and modestly rollback Iran’s nuclear program in return for some limited sanctions relief, Netanyahu has quieted down a bit and has set up a team to work with the U.S. on the precise terms for a final deal with Iran. I hope that Bibi doesn’t get too quiet, though. While I think the interim deal is a sound basis for negotiating a true end to Iran’s nuclear bomb-making capabilities, the chances of getting that true end are improved if Bibi is occasionally Bibi and serves as our loaded pistol on the negotiating table.

When negotiating in a merciless, hard-bitten region like the Middle East, it is vital to never let the other side think they can “outcrazy” you. The Jews and the Kurds are among the few minorities that have managed to carve out autonomous spaces in the Arab-Muslim world because, at the end of the day, they would never let any of their foes outcrazy them; they did whatever they had to in order to survive, and sometimes it was really ugly, but they survived to tell the tale. Anyone who has seen the handy work of Iran and Hezbollah firsthand — the U.S. Embassy and Marine bombings in Beirut, the assassination of Prime Minister Rafik Hariri in Lebanon, the bombing at Khobar Towers in Saudi Arabia, and the bombing of the Jewish Community Center in Buenos Aires — knows that the Iranians will go all the way. Never negotiate with Iran without some leverage and some crazy on your side. Iran’s leaders are tough and cruel. They did not rise to the top through the Iowa caucuses.

While you need some Obama “cool” to finalize a deal with Iran, to see the potential for something new and to seize it, you also need some Bibi crazy — some of his Dr. Strangelove stuff and the occasional missile test. The dark core of this Iranian regime has not gone away. It’s just out of sight, and it does need to believe that all options really are on the table for negotiations to succeed. So let Bibi be Bibi (up to the point where a good deal becomes possible) and Barack be Barack and we have the best chance of getting a decent outcome. Had Bibi not been Bibi, we never would have gotten Iran to the negotiating table, but without Barack being Barack, we’ll never get a deal.

Just the opposite is true on the Israeli-Palestinian front. Had Kerry not doggedly pushed Bibi and Palestinian President Mahmoud Abbas to the negotiating table, Bibi would not have gone there on his own. As Stanley Fischer, the widely respected former Bank of Israel governor, told a New York University forum on Tuesday: “The approach that we have to be strong, because if we’re not strong we will be defeated, is absolutely correct but it is not the only part of national strategy. The other part is the need to look for peace, and that part is not happening to the extent that it should,” the Israeli newspaper Haaretz reported.

I believe Europeans, in particular, would be more sympathetic to a harder-line Israeli position on Iran if they saw Israel making progress with the Palestinians, and if some of them did not suspect that Bibi wants to defuse the Iranian threat to make the world safe for a permanent Israeli occupation of the West Bank. Moreover, if Israel made progress with the Palestinians, it could translate the coincidence of interests it now has with Saudi Arabia and the Gulf Arabs — which is based purely on their having a common enemy, Iran — into a real reconciliation, with trade and open relations.

On the Iran front, Netanyahu’s job is to make himself as annoying as possible to Obama to ensure that sanctions are only fully removed in return for a verifiable end to Iran’s nuclear bomb-making capabilities. On the Israeli-Palestinian front, Obama’s job is to make himself as annoying as possible to Netanyahu. Each has to press the other for us to get the best deals on both fronts.

This is a rare plastic moment in the Middle East where a lot of things are in flux. I have no illusions that all the problems can be tied up with a nice bow. But with a little imagination and the right mix of toughness and openness on Iran and the Israeli-Palestinian issue, the Israeli prime minister and American president could turn their bitter-lemon relationship into lemonade.