A strong convergence is occurring in the Middle East between a rapidly deteriorating security environment in Iraq and Syria and a nuclear future whose fate remains unfixed. The focal point is the relationship between the United States and its longtime adversary in the region, the Islamic Republic of Iran. The secret history of Cold War détente offers a case study in how back-channel discussions at multilateral talks might help these two estranged powers resolve their differences, which would allow them to open a new chapter in U.S.-Iranian affairs.

It is imperative that U.S. and Iranian officials distinguish between political statements and real opportunities at this critical historical juncture. Recently, Iranian supreme leader Ayatollah Ali Khamenei warned the U.S. against intervening militarily in Iraq, where a lethal cocktail of Sunni rebels and Islamic extremists threatens the security and stability of Iran’s neighbor. In his statements, he accused Washington of harboring imperial designs that “seek[ed] an Iraq under its hegemony and ruled by its stooges.”

Earlier, Iranian President Hassan Rouhani had indicated that his government might be willing to work with the United States in efforts to bring stability to Iraq under certain conditions. A few days later, he declared his government ready to take the “final step” toward resolving the longstanding dispute over its nuclear program, “[i]f the international community recognizes Iran’s right for peaceful use of nuclear energy.”

Which statements should the Obama national-security team heed in its efforts to juggle two crises at once? Domestic audiences and the national interests of both states could cause these closely linked crises to deepen rather than transcend years of U.S.-Iranian mistrust. So, from where can the two sides draw reliable and accurate information as they contemplate more constructive relations following decades of mutual enmity?

The annals of nuclear diplomacy between the United States and the Soviet Union might afford a useful case study from which American and Iranian leaders could learn. The secret history of Cold War détente illustrates how low-level negotiations helped keep vital lines of strategic communication open.

In contrast to the conventional wisdom that Nixon and Kissinger masterminded Soviet-American détente, those who brokered the Nuclear Nonproliferation Treaty (NPT) during the presidency of Lyndon Baines Johnson in fact laid the groundwork for superpower cooperation.

Back then, it was the Vietnam War that was impeding efforts to stem the spread of nuclear weapons into such volatile regions as the Middle East. Moscow was keen to work with Washington in order to stop China, India, Japan, Israel and especially West Germany from acquiring the ultimate weapon, but Soviet leaders felt obliged by their past propaganda and watchful allies to take the Johnson administration to task for its political and military operations in Southeast Asia.

Multilateral talks at the Eighteen Nation Committee on Disarmament in Geneva, Switzerland therefore functioned as an invaluable backchannel for frank conversations. When Soviet mouthpieces assailed Johnson over Vietnam, Soviet arms-control negotiator Semyon Tsarapkin assured William “Bill” Foster, the director of the now defunct U.S. Arms Control and Disarmament Agency, that anti-American broadsides did not signal a “return to the Cold War” following the thaw brought about by the Cuban Missile Crisis and the signing of the Limited Test Ban Treaty.

The year was 1964 and the setting was a cold February day in Foster’s Geneva apartment, where the two men slipped away after a long plenary session to talk over vodka. Tsarapkin began by suggesting that “if the U.S. as the world’s gigantic power and also the large Soviet Union were to reach agreement, all troubles in the world could be readily controlled by us.”

In a lengthy cable addressed to the White House, among others, Foster related how positively the Soviet Union viewed the merits of superpower condominium amid the Sino-Soviet split, the Vietnam War, and a world increasingly awash in nuclear weapons:

He reiterated time and again that our two countries are self-sufficient and therefore have … no need to encroach upon each other, that they both bore great responsibility for what went on in [the] world and … they had to pay [the] price for this responsibility. He took [the] line that all other countries, including France, China, India, [Egypt], … even [the] G.D.R. [German Democratic Republic], were playing [the] U.S. and U.S.S.R. against each other and were trying [to] obtain advantage from differences and contradictions between them; they could do it in present circumstances, but if [the] U.S. and [the] U.S.S.R. were to agree with each other everybody else would have no choice but to fall in line.

Tsarapkin’s hypothetical resonates today. The Obama administration now finds its own geopolitical interests aligning awkwardly with those of its foremost antagonist in the Middle East. Both countries want a stable Iraq. Americans cringe at the prospect of a decade of blood and treasure spent buying a failed state. Iranians recoil at the notion of a return of Sunni control, or a civil war, in light of memories of their horrendous conflict with Iraq from 1980 to 1988, when it was still ruled by Saddam Hussein’s Sunni-dominated regime.

Both countries want to find an exit from an interminable nuclear controversy that will measurably limit Iran’s ability to break its legal commitments under the NPT by sprinting toward a nuclear capability while affording the Islamic Republic more than a modicum of autonomy in its nuclear sector.

The settlement’s terms must include real limits on Iran’s capacity to enrich uranium or reprocess plutonium. But political considerations will determine Khamenei and Rouhani’s willingness to abide controls.

To deter a U.S. intervention akin to Operation Iraqi Freedom and to forestall a failed or belligerent state next door are two cardinal reasons why Tehran would want a nuclear arsenal. Fostering cooperation with the United States with an eye toward bringing stability to the region can therefore help the Iranian regime justify effective restrictions on its nuclear program such as a smaller number of safeguarded centrifuges or tight controls on plutonium production at the Russian-built Arak reactors. In a virtuous cycle, the nuclear negotiations can themselves hasten the detoxification of U.S.-Iranian relations that will in turn diminish Tehran’s nuclear appetite.

This history of Cold War nuclear diplomacy suggests a new tactic that might open a crucial window for cooperation. Reports relate that Iranian diplomats and those of the P5+1 group composed of negotiators from the United States, the UK, France, Germany, Russia and China dine separately because of Islam’s prohibition against alcohol. Now that negotiations have resumed with a July 20 deadline fast approaching, U.S. Secretary of State John Kerry might instead direct Under Secretary of State for Political Affairs Wendy Sherman to sit down for tea with their Iranian counterparts. If reports that Kerry plans to embark for Vienna in the coming days (for purposes of participating in the concluding councils) are accurate, he too should raise a cup.

Meeting bilaterally with the Iranians before the last round of talks was a good first step. Now, both sides ought to seize the occasion to funnel demands, hypotheticals and possible compromises through the Vienna channel. They might be surprised to find that face-to-face encounters yield better results than official discourse composed for domestic audiences, especially given that the United States lacks an embassy in Tehran. Trust between nations, after all, must begin with trust between individuals.

Obama would be even wiser to heed such information. If history shows that honesty comes easier in the hallways of international convention centers than from behind lecterns at official press conferences, it also indicates that leaders ignore such sources of information to the detriment of their policies. Four years lapsed between those frank exchanges over drinks between Tsarapkin and Foster and the opening for signature of the NPT whose safeguards and principles the Obama administration is even now striving to uphold.

In summer 1964, when Foster informed the committee of principals charged with assigning priorities in U.S. nuclear policy of Moscow’s olive branch, Under Secretary of State George Ball and Ambassador to the Soviet Union Foy Kohler discounted Tsarapkin’s words. They believed that Moscow did not want a deal. The consequence was that U.S.-Soviet cooperation on nuclear nonproliferation and other security matters stalled for four years.

Today, neither side can afford to wait that long for a solution to emerge. Not while Iraq and Syria smolder and voices in Israel and the United States call for preemptive strikes against Iran’s hardened nuclear facilities.

Détente’s merits can be argued, but it will not happen if clear lines of communication are not established between two countries whose records in that department are inglorious at best. Nuclear negotiations with Iran can serve as both the means and an end by helping to descramble strategic dialogue while removing a massive impediment to cooperative relations—and all for the cost of a cup of tea.

Jonathan R. Hunt is a MacArthur Nuclear Security Fellow at the Center for International Security and Cooperation within the Freeman Spogli Institute for International Studies at Stanford University. He is writing a history of the golden age of global nuclear diplomacy during the Cold War.