It’s a classic case of brinkmanship bargaining: Iran and the West, each seeking to squeeze concessions from the other side, have decided to extend their nuclear negotiations to another round starting on June 17, a few weeks before a punishing new round of sanctions takes effect.

The deadlock was described at the conclusion of Thursday’s negotiating session in Baghdad by Catherine Ashton, the European Union’s chief diplomat and the West’s spokesperson: “It is clear that we both want to make progress, and that there is some common ground. However, significant differences remain.”

What’s the likelihood that this game of chicken will produce an acceptable deal? A skeptic would say that the chance is probably slim, given the level of mutual mistrust and the conviction on both sides that the best way to get an agreement is to tighten the screws. But because a military confrontation lies on the other side of diplomatic failure, both sides keep at it.

To try to imagine what a workable solution might look like, I spoke Thursday afternoon to Seyed Hossein Mousavian, a former member of the Iranian negotiating team who is now a visiting scholar at Princeton. I also read his remarkable new book, “The Iranian Nuclear Crisis: A Memoir,” which will be published next month.

Mousavian’s basic argument is that a deal is possible but only if it recognizes Iran’s rights as a signatory of the Non-Proliferation Treaty (NPT). In practice, this means that the West must drop its goal of preventing Iran from enriching uranium, which is permitted under the treaty, and instead focus on ensuring that Iran doesn’t build a nuclear weapon.

Mousavian quotes a vow Supreme Leader Ali Khamenei made in 2004: “I would resign if for any reason Iran is deprived of its rights to enrichment.”

We might wish that it were otherwise, but I think that Mousavian is correct that allowing Iran some enrichment activity is a necessary condition of a deal. Once that right is established, Mousavian thinks that Iran would agree to a “zero stockpile” of uranium enriched to the potentially dangerous 20 percent level. As an interim “confidence-building measure,” Iran would export its stockpile of 20 percent uranium beyond what it needs for domestic civilian use.

A deeper point made by Mousavian is that Iran is unlikely to agree to anything if it’s seen as doing so under duress. This contradicts the established wisdom in Washington, which is that Iran has come to the table only because sanctions are beginning to hurt.

The pressure track seems to me to have provided some leverage, but I also understand Mousavian’s point that Iran “won’t make major concessions under threats.” Successful diplomatic negotiations are always a process in which each side can claim some success, rather than one of demand and capitulation.

It’s useful to view recent negotiating history through Iranian eyes. Here’s what this optic reveals: In 2005 Khamenei removed his ban on negotiations with America; in 2009 Iran offered to export to the United States its uranium enriched to 20 percent, and it renewed this offer with greater specificity in 2010 and 2011; Iran accepted a Russian proposal last July to suspend further enrichment capacity and accept the International Atomic Energy Agency’s “additional protocol” for intrusive inspection. The Iranians think that they got nothing but more sanctions for these moves.

The more the West has tried to squeeze Iran, the more the Iranians have done precisely the things that infuriate the West. That may be because they’re determined to acquire nuclear-weapons capability, or because they resist pressure tactics. Either way, recent efforts to constrain Iran haven’t worked.

Mousavian argues that a nuclear deal is within reach, based on the twin of pillars of Iran’s rights as an NPT signatory and Khamenei’s religious edict banning nuclear weapons. But for real security, he contends, Iran and the United States must launch a parallel bilateral negotiation.

As an agenda for these breakthrough talks, Mousavian suggests two opening topics where the countries have identical interests: stabilizing Afghanistan under a non-Taliban government, and curtailing drug trafficking in the region. As evidence of Iran’s readiness, he cites an invitation made in February 2011 in Sweden for Marc Grossman, the top U.S. diplomat overseeing Afghanistan, to come to Tehran for talks. A U.S. source said that Washington proposed talks in Afghanistan instead, but Iran balked.

How much of what Mousavian says would hold up in practice? The best test is negotiations, and there the two sides have given each other another month to explore paths away from the brink.