The most significant diplomacy surrounding the opening of this year's UN General Assembly did not involve Syria but Iran. What was agreed with Tehran is potentially significant. Talks will focus on nuclear issues. The rationale was straightforward: if nuclear talks succeed, everything else is possible; if no nuclear deal is reached, nothing else will matter.
Also agreed is the basic structure of negotiations. The objective is to settle on the end-game, on what is often termed "final status" in peace talks. This will entail constraints on Iran's nuclear capabilities along with arrangements for monitoring. In return, economic sanctions that are doing serious damage to Iran's economy will be eased.
Once there is agreement on an end-game, the sides will negotiate the pace and sequencing for getting there. Thus implementation will be step by step, but the parties will know what the final step will require before they take the first one.
It is also understood that while the formal mechanism for talks will be multilateral involving the permanent members of the UN Security Council, Germany and the EU, the real negotiations will be bilateral, between the US and Iran.
All this progress should not obscure the many differences that could well preclude success.
First, it would be difficult to exaggerate the fundamental mistrust. Iranians and Americans each have their own historical narratives: the former about the US-backed coup ousting the Mossadegh government in 1953, the latter the hostage ordeal in the wake of the 1979 revolution. More important, I have yet to encounter the US expert who believes that Iran's nuclear programme is, as President Hassan Rouhani maintains, for peaceful – that is to say, energy-related – purposes, given that country's enormous oil reserves.
Reinforcing this scepticism are statements by Mr Rouhani. In his address last week to the UN he said that "nuclear technology has already reached industrial scale". Iran's nuclear infrastructure (at least what we know of it) includes some 18,000 centrifuges, multiple enrichment sites, large amounts of uranium enriched to various levels and a new reactor that, once operational, could be a source of plutonium, a second path to a bomb.
In my two meetings with Mr Rouhani and his foreign minister, I heard flexibility on the possibility of giving up uranium already enriched to higher levels – but no going back to the day when Iran had only a small number of centrifuges. So it is far from clear that what will be enough for Iran in the way of nuclear capacity will not be too much for Israel or the US.
A third concern is political. It was not simply that the cautious Mr Rouhani was unwilling to shake hands with Barack Obama. It was also that Mr Obama's UN address gave Iran quite a lot – no US desire for regime change; acceptance of Iran's right to a peaceful nuclear programme – but Mr Rouhani offered little in return. Friday's phone conversation between the two was therefore a symbolic as well as substantive development. There are doubts about Mr Rouhani's ability to compromise even if he wants to. Much depends on Ayatollah Ali Khamenei, the supreme leader, who is, by definition, supreme.
Mr Obama has his own political challenges. Negotiating an accord with Iran that trades constraints on its nuclear programme in exchange for easing of sanctions will be tough. Gaining congressional approval could prove even tougher. There will be opposition from those who believe the US was too generous and trusting, and from those who seek regime or broader policy change.
We will know soon enough. Both sides are in a hurry. The new Iranian leaders worry that time is against them. They fear that conservatives defeated in the June elections will rally, while the public will grow impatient if the sanctions-battered economy does not improve.
Americans worry Iran is using time to get closer to creating an infrastructure able to produce fissile material, weaponise it and put warheads on missiles. Israeli officials do not hide their belief that under Mr Rouhani Iran will "smile its way to the bomb".
All of which means this diplomatic dance will be no waltz. Sooner rather than later – certainly before next year is out – we should know if we will be toasting success or managing a crisis.
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