WHEN America extended the war against the jihadists of Islamic State (IS) to Syria on September 22nd, it seemed to have a strategy: maximise Sunni support to isolate and ultimately defeat the extremists. America would not co-operate with the regime of Bashar Assad. Instead it would build up moderate rebels to the point where, with American help, they could take on both IS and, eventually, Mr Assad’s forces. Five Sunni Arab states joined the air campaign in Syria, where Western friends declined to go. Across the border in Iraq, a new prime minister was installed with the promise to work harder to win over disgruntled Sunnis

The first fortnight of operations has proven messy, however. Though IS has been pushed back in some areas, it is still making advances in others. It has crept towards Baghdad, causing jitters in the city, and this week was close to winning the Syrian Kurdish enclave of Ain al-Arab (known to Kurds as Kobane) on the Turkish border. More worrying for America, hardly anyone in Syria is cheering. Some complain that, instead of bombing Mr Assad, America is attacking his enemies; others claim that it is hitting civilians rather than IS; still others spread the idea that the whole business is a war against Islam. Almost all the rebels—including groups such as Harakat Hazm that receive anti-tank weapons from America and its allies—have criticised America. This raises a troubling question: is America causing a backlash among the very people it needs to win over?

One cause of Syrian disquiet is that, as well as bombing IS, America also targeted Jabhat al-Nusra, one of the strongest groups fighting the Assad regime. America says it only bombed a faction, dubbed the “Khorasan group”, claiming it was planning imminent attacks on the West. Jabhat al-Nusra, is affiliated to al-Qaeda but is nevertheless accepted by more moderate groups for its fighting prowess. IS, by contrast, initially fought rebels and Kurds to carve out territory for its “caliphate”.

The danger is that, out of jihadist solidarity, Jabhat al-Nusra may now join forces with IS to confront the common American enemy. The two fell out in 2013. But since the air strikes they are said to have declared a truce. Both are trying to rally fighters and civilians to their cause— and against America and its allies—by portraying the bombing as a war against Islam. Their international reach is probably limited, but their call for revenge may inspire others. On September 24th Jund al-Khilafah, an Algerian jihadist offshoot that has pledged allegiance to IS, kidnapped and beheaded a 55-year-old French tourist.

There is a second, perhaps more corrosive impact on Syria as a whole. Many note that Mr Assad’s regime has killed many more people than IS, yet Syrian forces have not been touched by American bombs. “Assad kills tens of Syrians every day,” says a father of four from Aleppo province, pulling out his smartphone to show a picture of a dusty, bloody, dead child pulled from the rubble after a regime airstrike. “America spent three years rejecting our calls for weapons and a no-fly zone, but now won’t help us directly.” Syrians, he says, want help to fight on their own, rather than to rely on foreigners’ air strikes. Mainstream rebels complain that America has not co-ordinated its attacks with them. No bombs hit IS in eastern Aleppo, where its fighters threaten the rebel-held town of Marea, notes Hussam al-Marie, a spokesperson for moderate fighters. And the American plan to train at least 5,000 Syrian rebels has yet to get under way. No group has yet been asked to nominate personnel for training. “When we ask about this, we get more promises,” says a rebel who deals with the Americans. “We have heard a lot of them before.” America stands accused of compounding the agony of Syria’s civilians. Although its bombs are precision-guided, it faces allegations that its strikes have killed non-combatants. It has acknowledged that its rules to avoid civilian casualties are looser in Syria than those for drone strikes elsewhere. A grain silo was reported hit in the town of Manbij where, military officials say, IS had a logistics hub. The bombing of oil refineries may deny jihadists an important source of revenue, but it has driven up fuel prices in much of Syria. Rumours are rife that Mr Assad’s air force has bombed civilian areas close to military targets struck by America, creating confusion over who should be blamed. In any case, many Syrians think air strikes are not seriously hurting IS, which had already moved its men and equipment out of some of its bases before they were struck. “They’re like mosquito bites,” says a Syrian living in the Turkish city of Antakya.

Thankfully, from America’s perspective, few Syrian Sunnis regard IS as a desirable ally. And Syria’s sectarian divide is less deep than Iraq’s, so it should be easier to persuade Sunnis to work with other sects. In Iraq, by contrast, military intervention to help the Iraqi government, and to stop IS massacring Yazidis, an esoteric sect, means that America is often seen by Sunnis as the air force of the Shia and minorities. Despite the appointment of Haider al-Abadi to replace the discredited Nuri al-Maliki as Iraq’s prime minister, it is proving hard to prise Sunni tribes and former Baathists from the arms of jihadists who offer protection from, and a challenge to, Shia power. A recent Iraqi opinion poll found a gulf of perceptions between Iraqi Shias and Sunnis: whereas most Shias trusted the Iraqi army, Sunnis were overwhelmingly suspicious of it.

Anti-American griping by rebel groups may be intended to fend off accusations of being America’s pawns; in private, many rebels say they are “not unhappy” to see Jabhat al-Nusra hit; and many civilians dislike IS’s brand of extremism. To some analysts, there may be benefits in forcing zealous Islamists straddling the murky ground between extremists and moderates to decide where they stand. America and its allies could then train and arm moderate fighters with less fear that they will co-operate with jihadists. Yet the complaints carry a warning, too: unless America can convince the majority of Syrians that it is on their side, the biggest winners may be IS and Mr Assad. That was not the plan.