U.S. President John F. Kennedy’s skillful management of the Cuban missile crisis, 50 years ago this autumn, has been elevated into the central myth of the Cold War. At its core is the tale that, by virtue of U.S. military superiority and his steely will, Kennedy forced Soviet Premier Nikita Khrushchev to capitulate and remove the nuclear missiles he had secretly deployed to Cuba.

As Secretary of State Dean Rusk rhapsodized, America went “eyeball to eyeball,” and the Soviets “just blinked.” Mythologically, Khrushchev gave everything, and Kennedy gave nothing. Thus the crisis blossomed as an unabashed American triumph and unmitigated Soviet defeat.

Kennedy’s victory in the messy and inconclusive Cold War naturally came to dominate the politics of U.S. foreign policy. It deified military power and willpower and denigrated the give-and-take of diplomacy. It set a standard for toughness and risky dueling with bad guys that could not be matched — because it never happened in the first place.

Of course, Americans had a long-standing mania against compromising with devils, but compromise they did. President Harry Truman even went so far as to offer communist Moscow a place in the Marshall Plan. His secretary of state, Dean Acheson, later argued that you could deal with communists only by creating “situations of strength.” And there matters more or less rested until the Cuban missile crisis, when JFK demonstrated the strength proposition in spades, elevating pressures on his successors to resist compromise with those devils.

What people came to understand about the Cuban missile crisis — that JFK succeeded without giving an inch — implanted itself in policy deliberations and political debate, spoken or unspoken. It’s there now, all these decades later, in worries over making any concessions to Iran over nuclear weapons or to the Taliban over their role in Afghanistan. American leaders don’t like to compromise, and a lingering misunderstanding of those 13 days in October 1962 has a lot to do with it.

In fact, the crisis concluded not with Moscow’s unconditional diplomatic whimper, but with mutual concessions. The Soviets withdrew their missiles from Cuba in return for U.S. pledges not to invade Fidel Castro’s island and to remove Jupiter missiles from Turkey. For reasons that seem clear, the Kennedy clan kept the Jupiter part of the deal secret for nearly two decades and, even then, portrayed it as a trifle. For reasons that remain baffling, the Soviets also kept mum. Scholars like Harvard University’s Graham Allison set forth the truth over the years, but their efforts rarely suffused either public debates or White House meetings on how to stare down America’s foes.

From the outset, Kennedy’s people went out of their way to conceal the Jupiter concession. It started when the president’s brother, Attorney General Robert F. Kennedy, met Soviet Ambassador Anatoly Dobrynin on Oct. 27 to present the Jupiters-for-Soviet-missiles swap. He told Dobrynin: We’ll take the Jupiters out, but it’s not part of the deal, and you can never talk about it. The Soviets removed their missiles, the United States removed the Jupiters, and the secret held for 16 years, until a small paragraph in an Arthur Schlesinger book upon which few remarked.