The debate over the Iranian nuclear deal is not just a fight about present and future policy, but also a battle over the past. Both supporters and critics of the deal wield competing historical analogies. The question is: Are any of these parallels accurate?

For conservative opponents, the nuclear framework is a rerun of Munich and appeasement in the 1930s. On a beautiful fall day in 1938, British Prime Minister Neville Chamberlain returned from Munich to London, having agreed to hand over large parts of Czechoslovakia to Nazi rule in exchange for Adolf Hitler’s promise of peace. The relieved British throngs greeted Chamberlain by singing, “For he’s a jolly good fellow.” But appeasement only served to whet the Nazi appetite for further aggression. In time, the Munich Agreement became widely seen as a terrible mistake that paved the way for World War II and demonstrated the inherent folly of appeasing dictators.

Many conservatives fear that an autocratic regime is once again duping a naive Western leadership. “The deal being negotiated today is reminiscent of Munich in 1938,” said Senator Ted Cruz. His senatorial colleague Mark Kirk concluded that, “Neville Chamberlain got a lot more out of Hitler.”

But parallels with Munich quickly fall apart. First of all, the Iranian threat can’t be compared to that of Nazi Germany—a great power set on world domination. Furthermore, in 1938, Britain and France orchestrated a pact with the devil virtually alone. But now the entire permanent membership of the UN Security Council plus Germany (known as the P5+1) is negotiating collectively with Iran. And Senator Kirk is surely wrong on the relative compromises made by Chamberlain and Obama. In 1938, Hitler’s only real concession was not to start an immediate war. By contrast, in exchange for sanctions relief, Iran will have to accept some of the toughest restrictions ever imposed on a nuclear program.

In defending the nuclear deal, Barack Obama offered a very different historical parallel. “The American people remember that at the height of the Cold War, presidents like Nixon and Reagan struck historic arms-control agreements with the Soviet Union … despite the fact that that adversary not only threatened to destroy our country and our way of life, but had the means to do so.”

If the deal with Iran isn’t Munich, could it be Reykjavik? In 1986, U.S. President Ronald Reagan and Soviet Premier Mikhail Gorbachev met in the Icelandic capital to negotiate an arms-control agreement. The summit laid the groundwork for the 1987 Intermediate Nuclear Forces Treaty, which produced deep cuts to both sides’ nuclear arsenals, and helped bring about the end of the Cold War.

Might a bargain with Iran bring Tehran in from the cold? After all, the United States and Iran share some common interests in opposing the Islamic State in Iraq and Syria, and Taliban rule in Afghanistan.

But once again, the analogy is suspect. Iranian President Hassan Rouhani is no Gorbachev. The Soviet leader sought to take the hammer and sickle to sclerotic orthodoxies and defuse superpower antagonism. By contrast, Rouhani seeks to boost the Iranian economy and ease the country’s relations abroad—while maintaining the political system at home and continuing to back anti-Western forces, including Bashar al-Assad’s Syrian regime. Gorbachev was the decider in Moscow. Rouhani ultimately answers to Supreme Leader Ali Khamenei, who remains committed to theocratic rule. Gorbachev promised glasnost, or openness. The mullahs of Iran have engaged in extensive deception about their nuclear program.

Obama is on firmer ground by drawing a parallel with earlier Cold War bargains hammered out by John F. Kennedy and Richard Nixon. The Partial Test Ban Treaty of 1963 prohibited nuclear tests except those occurring underground. Meanwhile, the Anti-Ballistic Missile Treaty of 1972 limited the development of defenses against nuclear attack. No analogy is perfect, and there are plenty of obvious differences between superpower negotiations in the Mad Men era and parleying with Tehran today. But these cases all represent imperfect bargains with an autocratic opponent, which nevertheless stabilized the international system.

JFK and Nixon didn’t expect the treaties to suddenly end the Cold War. There were profound doubts about enforcing the terms of the agreements. And neither deal stopped the Soviets from engaging in acts of aggression, including the invasions of Czechoslovakia in 1968 and Afghanistan in 1979.

But the Cold War treaties diminished the odds of crisis or war. Kennedy and Nixon recognized that the United States could parley with Moscow and still pursue an overarching strategy designed to change its adversary. JFK said the Partial Test Ban Treaty “will not resolve all conflicts, or cause the Communists to forego their ambitions, or eliminate the dangers of war.” Nevertheless, it was a “victory for mankind” that would reduce nuclear testing and prevent the spread of nuclear weapons.

A deal with Iran is also a practical attempt to stabilize the international order. By freezing and rolling back key components of the Iranian program, there will be at least a year’s warning time before Iran could build the bomb. Any attempt by Tehran to cheat and break out of the deal would likely be widely seen as an act of infamy, triggering a strong international response.

Dialing down the mood of crisis surrounding Tehran’s nuclear program could provide opportunities for further progress in the region. For all its limits, JFK described the Partial Test Ban Treaty as “an important first step—a step towards peace, a step towards reason—a step away from war.” Obama said the U.S. goal was order in the Middle East, and the nuclear deal was “one place to start.”