OFFICIALLY, Saudi Arabia is pleased to see Iran shelve its nuclear ambitions in return for sanctions relief. But behind that thin veil lurks alarm about the potential empowerment of the Sunni kingdom’s long-standing Shia rival. “The Iranian regime is like a monster that was tied to a tree and has finally been set loose,” warns a column in Al Sharq al Awsat, a normally staid Saudi daily that reflects government views. Private opinions are no less dark. “Iran before the agreement was an enemy, a powerful hungry regime,“ says Hussein Shobokshi, a Saudi businessman and commentator. “After the agreement it has become a devil, a mad hulk with green eyes.”

Metaphors are one thing, actions another. On July 14th, the very day that Iran’s nuclear deal was clinched in Geneva, Saudi-backed forces were dealing their biggest blow yet in a campaign to contain what they see as an Iranian-sponsored insurgency in Yemen. Bolstered by Saudi air strikes, factory-fresh armoured cars and special forces from a Saudi-led coalition of Arab states, Yemeni fighters—loyalists to the government that was toppled in March—surged into the port city of Aden. Within three days they had chased the last of the rebels from Yemen’s second-biggest city, ending a messy four-month occupation.

The move is not only the first big setback for the Houthis, as the largely Shia Yemeni insurgent group is known. The Saudi coalition’s foothold in Aden may presage a redivision of Yemen, a country only united in 1990, into southern and northern halves, an arrangement Saudi Arabia prefers. The first aircraft to land at Aden’s reopened airport, on July 22nd, was a Saudi military transport bearing aid, more weapons and the commander of the Saudi navy.

Yemen is only the latest of many theatres in which Saudi Arabia and Iran have sparred over the three and a half decades since an Islamic revolution ended Iran’s own monarchy. The Saudis and their Gulf allies funded Saddam Hussein when he invaded Iran in 1980, while Iran’s proxy in Lebanon, Hizbullah, battled Saudi-backed militias during the 1975-90 Lebanese civil war. In 2011 Saudi Arabia and its allies poured troops into the neighbouring kingdom of Bahrain to help quell a popular revolt. The demands for democracy in a country that is 60% Shia were seen as an Iranian plot to gain power.

Ongoing wars in Iraq and Syria have opened more brutal battlegrounds. While Iran has spent as much as $20 billion, by some estimates, to prop up the government of Bashar al-Assad, a recent increase in Saudi backing for his motley foes is widely viewed as explaining a series of military setbacks for the increasingly beleaguered Syrian regime.

Accusing Iran of fuelling unrest among Shias across the region, including among the kingdom’s own 10% Shia minority, Saudi rulers have for decades given free rein, as well as funding around the globe, to Sunni preachers spewing venom against the rival, smaller branch of the faith. A recent trove of Saudi diplomatic documents revealed by the whistle-blowing group WikiLeaks exposes a near-obsessive fear of Shia influence. In one cable, the kingdom’s embassy in the Egyptian capital, Cairo, warns that the change of a green-coloured shroud for a black one to cover a Sufi saint’s tomb reflects a creeping Shia tide.

The fears are mutual. Iranian officials mutter that Islamic State (IS) and other Sunni jihadist groups are Saudi pawns. Nuri al-Maliki, the Iran-backed former Iraqi prime minister whose antipathy to Sunnis is widely seen as having paved the way for IS’s rise, suggested, absurdly, that Saudi Arabia be annexed by the UN because it had “lost control” of Wahhabism, the root cause of terrorism.

Rather than seeing the reduction of an Iranian nuclear threat as an advantage, the Saudi government frets instead that its oldest ally, America, is poised to abandon the kingdom and appoint Iran as its new regional policeman. These worries explain a barrage of official American messages and visits intended to smooth ruffled feathers. John Kerry, the American secretary of state, plans to parley with Gulf leaders next month, following on the heels of the secretary of defence, Ashton Carter, who was there this week.

“We believe if you are going to push back against Iran, it’s better to push back against an Iran without a nuclear weapon than with one,” says Mr Kerry in defence of the deal. The Saudis, whose new king, Salman, has given his son Muhammad sweeping powers to prosecute military action, will want to push back hard. They will also want to push back fast, before Iran realises a windfall of at least $100 billion from frozen funds released by the end of sanctions. That portends little relief from the heat in places like Syria and Yemen.