The U.S.-Iranian relationship is worse than ever before. Over the last four months, the American and Israeli militaries have waged full-scale war against the Islamic Republic, including by assassinating much of its political and military leadership. Iran has retaliated by attacking U.S. military bases, infrastructure in Gulf Arab states, and Israel. The two sides struck a cease-fire deal in early April, and in June they signed a memorandum of understanding designed to end the conflict. But those deals have, so far, failed; Iran and the United States have continued to exchange fire. They remain far apart on core disputes, including those related to Iran’s nuclear program, the Strait of Hormuz, and sanctions relief. As a result, many analysts are skeptical that the parties can eventually achieve a permanent deal.

The increasingly sharp hostilities since the memorandum came into effect demonstrate that this skepticism is well-founded. Rather than marking a new chapter in U.S.-Iran relations, the two sides remain mired in the old. They are trading accusations that the other is operating bad faith and claiming that each is breaching the agreement they reached in April. They are engaging in a fitful dialogue largely conducted through third parties, rather than speaking directly. And their continued use of military force proves that they are willing to up the ante. There were more than 300 U.S. strikes against Iran in recent days. Tehran has retaliated against at least five regional states, as well as multiple ships transiting the Strait of Hormuz.

Yet paradoxically, the war may have created a moment of opportunity for Iran and the United States to repair their broken relationship. That is because the conflict has descended into a mutually unsatisfying stalemate. Washington is clearly unable to topple the Islamic Republic, to compel it to give up its nuclear program, to make it stop supporting its regional allies, or to get it to give up control over the Strait of Hormuz. Tehran is unable to force the United States to vacate its backyard or to abandon its use of coercive economic and military tools. The war, in other words, has made it plainly apparent that neither government can deliver a knockout blow to the other at an acceptable cost—and that unmanaged hostility has become too costly and perilous.

In both capitals, many officials are starting to realize this fact, even as the fighting continues. As a result, some decision-makers in each have started looking for ways to coexist. For the first time in nearly a decade, senior American and Iranian officials have met directly as part of negotiations. They are discussing meaningful compromises. And the two sides may agree to set up a hotline that would connect their militaries, designed to help manage conflict before it spirals. If they make good on this tentative pledge, it will be the first such U.S.-Iranian channel since revolutionaries stormed the American embassy in Tehran, in 1979.

These efforts might well fail. The memorandum, after all, is on the verge of collapse. Each country is home to formidable forces that oppose diplomacy and prefer confrontation. There will certainly be limits to just how much these two nemeses can achieve via engagement. But both sides may eventually arrive, through sheer exhaustion, at the same reluctant conclusion: the old playbook has failed. Change will still be difficult, but it is imaginable.

The 2015 Joint Comprehensive Plan of Action was the last serious attempt to stabilize and reset U.S.-Iranian relations. Formally, it was a narrow deal. Iran pledged to restrict its nuclear program and accept increased international inspections. In exchange, the United States offered limited sanctions relief. But politically, the JCPOA was a larger wager. If the status of Iran’s nuclear program could be solved, officials........

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