THESE are early days, but the campaign that Barack Obama announced almost exactly a month ago to “degrade and ultimately destroy” Islamic State is not going well. In both Syria and Iraq, IS is scoring victories against the West and its Sunni Arab allies. The coalition’s strategy is beset by contradictions and self-imposed constraints, with two of the worst offenders being the two countries that could do the most to degrade IS: America and Turkey. The coalition must rise above these shortcomings, or IS will end up being validated in the eyes of could-be jihadists—the very opposite of what the coalition’s leaders set out to achieve. As The Economist went to press, the strategically important Kurdish town of Kobane, on the border with Turkey, had been entered by heavily armed IS fighters and surrounded on three sides. Coalition air strikes have delayed the town’s fall, but probably by only a few days. If Kobane succumbs there will be a chorus of demands for a redoubled coalition effort, offset by dire warnings of the dangers of mission creep.

IS poses a threat to the entire Middle East and is potentially a source of terrorism against the West. So more effort makes sense, but only if the campaign can resolve its contradictions.

That task starts with Turkey. Despite a vote in the parliament in Ankara on October 2nd, authorising the country’s forces to operate in Syria, Turkey’s president, Recep Tayyip Erdogan, is engaged in an elaborate juggling act. He says, correctly, that air strikes alone cannot overcome IS and that every means must be used to defeat it. But although he has tanks parked along the border, he refuses to help the Kurds, whom he sees as his enemies. Indeed, even as he leaves Kobane to its fate, his riot police are killing Kurds protesting within Turkey. Mr Erdogan seems wary of offering anything more than rhetorical Turkish support for the coalition, unless America enforces a buffer and no-fly zone on the Syrian side of the border. He is also insisting that America should make removing the Assad regime a higher priority than tackling IS.

America’s strategy is also beset with tensions. Although it wants to see Mr Assad go, it is reluctant to join that fight for now, partly because success in Iraq depends on persuading the government in Baghdad to become sufficiently inclusive to woo back the alienated Sunni tribes. And for that it needs the help of Iran, Mr Assad’s closest ally. Meanwhile, America’s collaboration with the Shia-led government has not made it any easier to win over suspicious Sunnis. While air strikes have helped the Kurds regain some ground from IS, security in Sunni-dominated Anbar province has continued to deteriorate. After IS fighters overran some Iraqi army bases and seized control of Abu Ghraib, within shelling range of Baghdad’s international airport, America sent in Apache attack helicopters to hit IS targets along the road that runs west of Baghdad to the IS stronghold of Falluja. Calling up the Apaches—not boots on the ground, perhaps, but certainly boots in the air—is an admission that high-flying fast jets have their limitations.

The coalition is also up against the law of unintended consequences. After its first big attack in Syria, it has targeted the oil refineries which help finance IS’s activities and other bits of IS infrastructure. But military action has also driven the dwindling band of “moderate rebels”—the ones that America aims to train and arm—into the embrace of jihadist groups, such as the al-Qaeda affiliate Jabhat al-Nusra, which now portray the coalition as an anti-Sunni stooge of the Assad regime.

Kurds all the way

John Allen, a former general and Mr Obama’s special envoy for the coalition against IS, flew to Ankara this week in an effort to find common ground with the Turks. Nobody would claim there are easy answers for either Mr Obama or Mr Erdogan, but both are guilty of willing an end while withholding the means to secure it. In Mr Erdogan’s case, it is nonsense to claim he backs the effort to destroy IS while he leaves Kobane’s Kurds to be slaughtered. If the town falls, both Turkey’s reputation and its security will suffer a grievous blow. Better to act as a full member of the coalition and use the goodwill this generates to influence it from the inside. Mr Erdogan should use his troops to save Kobane—and give America permission to fly from the giant NATO airbase at nearby Incirlik.

For his part, Mr Obama needs to face up to two things. First, most of the coalition wants to see the back of Mr Assad: his serial brutalities against his own people have appalled Sunnis everywhere. Russia and Iran have hinted that they would accept a more pragmatic military figure in his place if their interests were respected. Mr Obama should work on that. Second, the fight against IS cannot succeed without competent troops on the ground to guide coalition aircraft to their targets, pursue enemy leaders and take and hold territory. That calls for the use of special forces in greater numbers and on more missions. Other troops need to be embedded in the better Iraqi units to train and mentor them. When Martin Dempsey, the chairman of the joint chiefs of staff, called for that, he was slapped down by Mr Obama. With such actions the president means to look resolute, but the people he reassures most are the jihadists.