LAUSANNE, Switzerland � It was just one of hundreds of arguments between American and Iranian officials as they tried to hash out what may prove to be one of the hardest-to-negotiate arms control agreements in history. But it spoke volumes about how two countries that so deeply distrust each other managed to strike a tentative deal.


After�President Obama�revealed the existence of a secret, deep-underground enrichment operation near the sacred city of Qum in late 2009, the White House demanded that it be dismantled and closed. In defiance, the Iranians stuffed the facility, called Fordo, with 3,000 centrifuges � a huge issue for American and Israeli military planners because it is impervious to all but the largest bunker-buster bombs.


Iran�s supreme leader, Ayatollah�Ali Khamenei, also decreed that no nuclear facilities would be closed. So when negotiations turned to Fordo�s fate, the Iranians insisted that the centrifuges had to stay and the Americans said they all had to come out.


The compromise � one of the most painful, an American official acknowledged on Thursday night � was that 1,000 centrifuges would remain. But they are to have no fissile material, the makings of a nuclear weapon.


Instead, they will spin another element, for medical isotopes. Still, the official acknowledged the optics were bad: �Having even one centrifuge in Fordo is hard.�


After two years of secret diplomacy, then gradually accelerating engagement, then eight straight days and several all-nighters of negotiations this week in Lausanne, Switzerland � so intense that officials showed up at breakfast looking like they had just wandered off a 20-hour flight � the accord reached here on Thursday was filled with provisions like that.


The agreement calls for Tehran to slash its stockpile of nuclear materials and severely limit its enrichment activities, theoretically bringing the time it would take to produce a nuclear weapon to a year � a significant rollback from the current estimate of two to three months.


Both sides made significant compromises. For the United States, that meant accepting that Iran would retain its nuclear infrastructure in some shrunken form. For Iran, it meant severe limits on its production facilities and submitting to what Mr. Obama has called the most intrusive inspections regime in history.


It is still far too early to tell if the compromises will survive the next and final negotiating round, or review in Washington and Tehran. The timing of sanctions relief remains unresolved, for example, and already the two sides are describing it in different terms.


But the events of the last two years, and particularly the past week, offer some fascinating insights into what happens when two countries that have barely spoken with each other for 35 years � and have a long and troubled history of mistrust, sabotage, lies and violence � all but move into the same hotel room to try to figure out how they are going to get along.


It is fairly certain there will be a lot more wrangling in the next three months as the negotiators seek to wrap up a final, comprehensive treaty. That is because the negotiators left the Beau Rivage Hotel with astoundingly high bills � suites run more than $1,500 a night � but not an agreed-upon document detailing Iran�s commitments and those of the United States and its negotiating partners.


Wherever Wendy Sherman, the lead American negotiator, traveled in the ornate hotel here, she was trailed by a whiteboard, where the Iranians and the Americans marked down their understandings, sometimes in both English and Persian.


The board served a major diplomatic purpose, letting both sides consider proposals without putting anything on paper. That allowed the Iranians to talk without sending a document back to Tehran for review, where hard-liners could chip away at it, according to several American officials interviewed for this article, who all spoke on the condition of anonymity to discuss internal deliberations.


�It was a brilliantly low-tech solution,� one White House official said. (It also had its drawbacks. One American wrote on it with a regular marker, then had to scrub hard to wipe out some classified numbers.)


And it was far removed from the first year of Mr. Obama�s presidency when, one of his top aides recalled a few years ago, there were more Situation Room meetings on Iran than any other topic. By the end of his first year in office, the president had come to some big conclusions.


If Iran got the bomb, classic �containment� would not work; the Sunni Arab states, starting with Saudi Arabia, would try to match the effort. Refusing to negotiate unless all the centrifuges stopped spinning, the strategy of the Bush administration, also seemed futile; Iran had a few hundred working centrifuges in 2003, thousands when Mr. Obama took over and 19,000 now.


Insisting that Iran dismantle everything would not work, either; that would kill a negotiation before it started. And bombing would not work, at least not for very long. As William J. Burns, the deputy secretary of state who led the secret effort to establish relations with Iran�s new president, Hassan Rouhani, put it recently: �You can�t bomb knowledge. And there�s nothing we could destroy that they couldn�t rebuild in a few years.�


Mr. Obama, by all accounts, immersed himself in the technical details, beginning with the giant centrifuge hall at Natanz, when he had to approve wave after wave of cyberattacks there. It was hoped that those attacks, combined with economic sanctions, would force Iran to see the folly of continuing on its path.


Back then, the thinking was that Iran could have only a token production capability. Over time, though, the administration�s objectives became less ambitious.


As the negotiations sputtered forward, it became clear that to reach an agreement at all, Iran would have to be able to preserve a narrative of not backing down, not dismantling.


Mr. Obama got deep into the technical compromises to political problems. He read briefings on three different proposals for how to convert a heavy-water reactor at Arak so that it could remain in operation without churning out plutonium waste that could be used in a bomb. He often delved into the workings of inspection regimes.


But as the talks hit one deadline after another, the administration had to compromise more. Instead of maintaining strict limits throughout the life of a 15-year accord, for example, it began to talk about keeping the toughest limits � the ones that would extend to a year the time Iran needed to produce enough nuclear material for a bomb � in place for at least 10 years.


As Secretary of State John Kerry prepared to return to the negotiations in Lausanne last month, the French were openly questioning whether he and his team were so invested in the deal that they might make unwise compromises in order to meet an artificial deadline at the end of March.


�You hear that kind of stuff and you want to say, �Why don�t you sit at the table for months on end and see if you do any better?� � one of Mr. Kerry�s aides snapped when told of the critique.


As the talks grew more intense in the past two months, the Iranians decided to bring in their minister of atomic energy, prompting Mr. Obama to send Ernest Moniz, his energy secretary and one of the nation�s leading nuclear scientists. This changed the dynamic. The two men set up a separate process and, as one senior administration official said, �they treated these matters as scientific problems.�


With so many moving parts, Ms. Sherman, one of the most organized of diplomats, continued rolling out her whiteboards, a stark contrast with the elegance of the rooms they were meeting in at the Beau Rivage. But each issue that got crossed off seemed to be replaced by two more. Meetings went later and later.


Mr. Kerry was clearly feeling a bit caged: He went for bicycle rides three times (twice he had to return to take a call from the president). He went for crepes down the street and showed up at a bar to help celebrate the birthdays of some American reporters. Inside the negotiating rooms, an espresso machine constantly buzzed, as the Iranians and Americans tried to stay awake.


But when the deadline of March 31 came and went, quitting was not an option. �The trick was getting it to come together � you can see it, you see the deal,� a senior administration official said. �You know what the elements are. But knocking it out is another thing altogether.�


The Iranians knew the deadline meant a lot to Mr. Kerry � who needed to show progress to Congress � but it meant nothing to them. He, in turn, kept scheduling his departure, perhaps as a pressure tactic. His team deposited their luggage for loading onto the plane three times, only to find it returned hours later.


After an all-night round of negotiations on Wednesday, his counterpart, Mohammad Javad Zarif, was asked how much sleep he got. �Two hours,� he said. �And I was the lucky one.�


The last tradeoffs were painful. When the Iranians insisted on keeping some centrifuges at Fordo, Mr. Obama approved the concession after Mr. Moniz assured him the facility, devoid of fissile material under the accord, would pose no threat. His credibility carried the day. And administration officials were struck by the fact that Iran was willing to waste 1,000 centrifuges, essentially spinning uselessly, to preserve national pride.


The same thing happened in finding a solution for the Arak heavy-water reactor, which they agreed to redesign. �Moniz said this will not produce any weapons-grade plutonium,� said a senior American official, and that if the Iranians cheated it would be detectable right away.


At the White House, Mr. Obama was pressing intelligence agencies for a report on the real intentions of Ayatollah Khamenei, who would cast the sole deciding vote on any deal in Iran. He never got a persuasive consensus: �Frankly, that is almost unknowable,� the official said.


Some of the last issues were just punted to the next round, including the timetable for lifting sanctions and the specifics of how Iran will dispose of a large stockpile of uranium.


Complicating things further, the Iranians did not want to publish a list of agreed upon points. So it was agreed that each side would put out its own � as long as they did not directly contradict each other.


But the two documents left room for differences. As Mr. Kerry stepped to the microphones on Thursday and talked about all the limits on Iran, and how some would last 15 years, others 25, a few for much longer, Mr. Zarif had a different spin.


�We will continue enriching, we will continue research and development, our heavy water reactor will be modernized, and our facility in Fordo will remain open,� he said.


By The New York Times