Right now, a thousand pundits and politicians are debating the details of Thursday’s framework nuclear deal with Iran. That’s fine. I think the details are far, far better than the alternative—which was a collapse of the diplomatic process, a collapse of international sanctions as Russia and China went back to business as usual with Tehran, and a collapse of the world’s ability to send inspectors into Iran. But ultimately, the details aren’t what matters. What matters is the potential end of America’s 36-year-long cold war with Iran.

For the United States, ending that cold war could bring three enormous benefits. First, it could reduce American dependence on Saudi Arabia. Before the fall of the shah in 1979, the United States had good relations with both Tehran and Riyadh, which meant America wasn’t overly reliant on either. Since the Islamic Revolution, however, Saudi Arabia has been America’s primary oil-producing ally in the Persian Gulf. After 9/11, when 19 hijackers—15 of them Saudis—destroyed the Twin Towers, many Americans realized the perils of so great a dependence on a country that was exporting so much pathology. One of the unstated goals of the Iraq War was to give the United States a large, stable, oil-producing ally as a hedge against the uncertain future of the House of Saud.

What George W. Bush failed to achieve militarily, Barack Obama may now be achieving diplomatically. In recent weeks, American hawks have cited Saudi anxiety about a potential Iran deal as reason to be wary of one. But a big part of the reason the Saudis are worried is because they know that as U.S.-Iranian relations improve, their influence over the United States will diminish. That doesn’t mean the U.S.-Saudi alliance will disintegrate. Even if it frays somewhat, the United States still needs Saudi oil and Saudi Arabia still needs American protection. But the United States may soon have a better relationship with both Tehran and Riyadh than either has with the other, which was exactly what Richard Nixon orchestrated in the three-way dynamic between Washington, Moscow, and Beijing in the 1970s. And today, as then, that increases America’s leverage over both countries.

Over the long term, Iran may also prove a more reliable U.S. ally than Saudi Arabia. Iranians are better educated and more pro-American than their neighbors across the Persian Gulf, and unlike Saudi Arabia, Iran has some history of democracy. One of the biggest problems with America’s Mideast policy in recent years has been that, from Saudi Arabia to Pakistan to Egypt, the governments the United States supports preside over populations that hate the U.S. Thursday’s nuclear deal, by contrast, may pave the way for a positive relationship with the Iranian state that is actually undergirded by a positive relationship with the Iranian people.

Which brings us to the second benefit of ending America’s cold war with Iran: It could empower the Iranian people vis-à-vis their repressive state. American hawks, addled by the mythology they have created around Ronald Reagan, seem to think that the more hostile America’s relationship with Iran’s regime becomes, the better the United States can promote Iranian democracy. But the truth is closer to the reverse. The best thing Reagan ever did for the people of Eastern Europe and the U.S.S.R. was to embrace Mikhail Gorbachev. In 1987, American hawks bitterly attacked Reagan for signing the INF agreement, the most sweeping arms-reduction treaty of the Cold War. But the tougher it became for Soviet hardliners to portray the United States as menacing, the tougher it became for them to justify their repression at home. And the easier it became for Gorbachev to pursue the policies of glasnost and perestroika that ultimately led to the liberation of Eastern Europe and the disintegration of the U.S.S.R.

Iranian President Hassan Rouhani, like Gorbachev, wants to end his country’s cold war with the United States because it is destroying his country’s economy. And like Gorbachev, he is battling elites who depend on that cold war for their political power and economic privilege. As Columbia University Iran expert Gary Sick recently noted, Iran’s hardline Revolutionary Guards “thrive on hostile relations with the U.S., and benefit hugely from sanctions, which allow them to control smuggling.” But “if the sanctions are lifted, foreign companies come back in, [and] the natural entrepreneurialism of Iranians is unleashed.” Thus “if you want regime change in Iran, meaning changing the way the regime operates, this kind of agreement is the best way to achieve that goal.”

The best evidence of Sick’s thesis is the euphoric way ordinary Iranians have reacted to Thursday’s agreement. They’re not cheering because they want Iran to have 6,000 centrifuges instead of 20,000. They’re cheering because they know that opening Iran to the world empowers them, both economically and politically, at their oppressors’ expense.

Finally, ending the cold war with Iran may make it easier to end the civil wars plaguing the Middle East. Cold wars are rarely “cold” in the sense that no one gets killed. They are usually proxy wars in which powerful countries get local clients to do the killing for them. America’s cold war with the U.S.S.R. ravaged countries like Angola and El Salvador. And today, America’s cold war with Iran is ravaging Syria and Yemen.

When America’s relationship with the Soviet Union thawed, civil wars across the world petered out because local combatants found their superpower patrons unwilling to send arms and write checks. The dynamic in the Middle East is different because today’s cold war isn’t only between Iran and the United States, it’s also between Iran and Sunni Arab powers like Saudi Arabia and Egypt, neither of which seems particularly interested in winding down the civil wars in Syria and Yemen. Still, a different relationship between the United States and Iran offers a glimmer of hope. In Syria, for instance, one reason Iran has staunchly backed Bashar al-Assad is because it fears the fierce hostility of his successors. The United States cannot entirely alleviate that fear, since some of the groups battling Assad—ISIS, most obviously—are fiercely hostile to Iran and to Shiites in general. But if Iran’s leaders knew that at least the United States would try to ensure that a post-Assad government maintained good relations with Tehran, they might be somewhat more open to negotiating a transfer of power in Syria.      

Clearly, the United States should push for the best nuclear deal with Iran that it possibly can. But it’s now obvious, almost three decades after Reagan signed the INF deal with Gorbachev, that it’s not the technical details that mattered. What mattered was the end of a cold war that had cemented Soviet tyranny and ravaged large chunks of the world. Barack Obama has now begun the process of ending America’s smaller, but still terrible, cold war with Iran. In so doing, he has improved America’s strategic position, brightened the prospects for Iranian freedom and Middle Eastern peace, and brought himself closer to being the kind of transformational, Reaganesque president he always hoped to be.