This weekend's agreement between Iran and Western powers, which increases Iran's distance from a nuclear weapon, is the most significant breakthrough in their nuclear dispute for 10 years.
But for Israel, Saudi Arabia and the other Arab monarchies, the photographs of their US and European allies celebrating a deal with their historic rival Iran have some disturbing implications.
The response has not been universally hostile. The United Arab Emirates said the agreement could support "the stability of the region", and Bahrain's foreign minister said it "removes fears from us, whether from Iran or any other state".
Saudi Arabia was shocked when the US suddenly cancelled planned missile strikes against the Syrian regime, squandering what Riyadh saw as the best opportunity to roll back Iranian influence in years”
But others were less positive. Israeli Prime Minister Benjamin Netanyahu insisted that the deal was a "historic mistake" that "turns the world into a much scarier place".
A Saudi foreign policy adviser warned that the West's quid-pro-quo for the deal was "giving Iran more space or a freer hand in the region". What explains this angst?
Since the Iranian revolution of 1979, Israel and the Arab monarchies have viewed Iran as a major threat. Iran has given money and sophisticated missiles to militant groups on Israel's periphery, the most powerful of these being Lebanon's Hezbollah.
The Arab monarchies argue that Iran has subverted their Sunni-led and mostly Sunni-majority nations by supporting disaffected Shia communities.
In 2003, the US-led invasion of Iraq transformed it from an Iranian enemy to an Iranian ally. In 2011, the US stood by as another staunchly anti-Iranian regime in Egypt was toppled.
More recently, Saudi Arabia was shocked when the US suddenly cancelled planned missile strikes against the Syrian regime, squandering what Riyadh saw as the best opportunity to roll back Iranian influence in years.
That Saudi Arabia found out about the cancellation from CNN, rather than being told by American officials, added insult to injury.
For these countries, the nuclear diplomacy is therefore about more than just the nuclear dispute. They worry that the West has prematurely eased the pressure before Iran completely surrendered, leaving Iran with enough nuclear infrastructure to allow it to build a bomb in the future.
They will be particularly vexed that the agreement envisages allowing Iran to continue enrichment of uranium (albeit under heavy curbs) indefinitely, something that Israel in particular had opposed.
But their greater fear is that this opens the door to a US accommodation of Iran in the region which, when combined with a growing US focus on Asia, will lead to a progressive erosion of America's inclination and ability to protect Israeli and Arab interests against Iranian meddling.
In some ways, this fear of abandonment is a rekindling of old anxieties. On a recent trip to the Gulf, an official from one Arab country told me that "we can remember a time when the US was closer to Iran than Saudi Arabia", referring to the reign of the Shah of Iran.
These fears are overwrought, but they are sincerely and widely held in the Middle East. They are reinforced not just by the fact of this deal, but also the way it was done.
It is reported that the US had been in secret bilateral talks with Iran since before the June election of Iranian President Hassan Rouhani - including over the period it cancelled the Syria strikes - and that Saudi Arabia tipped Israel off about these clandestine contacts.
This highlights two interesting trends. First, Saudi and Israeli perceptions are increasingly converging, despite the fact that Riyadh does not even recognise Israel as a state.
Second, US allies are increasingly convinced that US-Iran co-operation will inevitably come at Arab and Israeli expense - a view that will harden if Iran is now included in US and Russia-led peace talks for Syria.
How can these countries respond? Israeli officials have warned that they are not bound by the terms of the deal - an implicit threat that the military option remains on the table - and Saudi officials intimate that they can procure a nuclear weapon for themselves from Pakistan.
Neither of these steps is likely for the duration of this interim deal. As Israel's former army intelligence chief Amos Yadlin put it: "In the coming six months the legitimacy of an attack will diminish".
But the US and Israel have previously co-operated on cyber-attacks against Iran, and Israel is widely believed to have assassinated Iranian nuclear scientists. Such covert action should not be ruled out, though it would anger Washington and all those who negotiated this agreement.
If a longer-term settlement does not follow, and Iran renews its nuclear expansion, then the risk of Israeli airstrikes will grow significantly.
It is implausible that Saudi Arabia will offer direct military assistance to any Israeli attack, as Britain's Sunday Times newspaper suggested this month, but it might secretly grant over-flight rights to Israeli bombers.
Saudi-Israeli intelligence contact is also likely to flourish, particularly as the two countries look for any sign that Iran is cheating on the deal. But neither country can afford to push the US too far away.
The Geneva agreement is a modest step that leaves much work still to be done. But for some of America's allies, it is a troubling sign of things to come. Their priority will be to ensure that this nuclear thaw does not now turn into a regional realignment.