THE repertoire of new horrors keeps expanding. On February 3rd the jihadists of Islamic State (IS) released a video showing the immolation of Flight Lieutenant Moaz al-Kasasbeh, a Jordanian pilot captured after he ejected from his F-16 jet, over Syria in December. The sickening footage appears calculated to attract potential IS recruits; scare and provoke its enemies into actions that would feed IS’s propaganda; and create cleavages between the leaders and populations of countries who have joined in coalition against it.

Sure enough, within a few hours Jordan responded by hanging two convicted terrorists, including one whose freedom IS had demanded in exchange for Lieutenant Kasasbeh. But in other respects IS may have miscalculated. Jordan, which along with the United Arab Emirates (UAE) had stopped flying sorties against IS after the pilot’s capture, vowed a “severe” response. The Jordanian people, many of whom had just days earlier been protesting the monarch’s decision to join the coalition against IS, now seem united in outrage and demands for revenge. Even jihadist groups have expressed outrage at the killing.

Despite the ghoulish propaganda, the coalition can claim to be making slow progress. It is six months since Barack Obama gathered 60-odd countries into a coalition to “degrade and ultimately destroy” IS. Since the first air strike in Iraq on August 8th, the campaign has extended into Syria and widened to include arming and training allies such as Syrian and Iraqi Kurds, and Iraqi government forces.

America’s Central Command claims that about 6,000 IS fighters have been killed, including up to half the group’s “top commanders”. Some reckon it has 30,000 fighters in fray. At the end of January Kurdish fighters in Kobane, a Syrian town on the border with Turkey, said that they had expelled IS after four months of grim fighting with help from coalition bombers.

More than 1,000 IS fighters are thought to have been killed in that battle. Syrian Kurds have also extended their control into surrounding villages previously held by IS. Rebels in provinces to the west of Kobane say their front lines with IS have been quiet, suggesting that the jihadists are struggling to fight on multiple fronts.

The biggest setback appears to have been to the aura of invincibility that IS acquired last year when its advance through Iraq and Syria seemed unstoppable. Although IS still controls an area of Syria and Iraq about the size and population of Jordan, it has been unable to expand into areas of Iraq where Shias or Kurds are a majority. Threatening Baghdad or Erbil now appears beyond IS’s capacity.

IS sees no distinction between Iraq and Syria, as the coalition does. As the group gets squeezed in Iraq, it is likely to expand into Syria where there is little the coalition could do but increase the number of air strikes. The population of potentially-friendly Sunnis is far greater than in Iraq and the atrocities of Bashar Assad’s regime continue to stir Sunni resentment. Outside the Kurdish areas there are no local forces to partner with. Until the coalition can resolve its conflicting interests in Syria, above all how it intends to get rid of the Assad regime, IS will at most be contained.

Foreign fighters appear to be flowing in to replenish losses as fast as ever, reckons Rami Jarrah, a Syrian journalist who lives on Turkey’s border with Syria. In January the International Centre for the Study of Radicalisation and Political Violence, a London-based think-tank, suggested there were at least 20,000 foreign jihadists, surpassing the number that flocked to defeat the Soviets in Afghanistan in the 1980s.

On the ground the battlefront remains fluid. In November Iraqi government forces, with help from coalition air power, retook Baiji, the site of Iraq’s biggest oil refinery, in a major reverse for IS. A month later they had lost it again. Though IS appeared to have consolidated its grip on the mainly Sunni province of Anbar, some Shia militias, invited in perhaps surprisingly by local Sunni tribal leaders, have made advances. In late January, Iraqi government and Shia forces pushed IS out of its remaining stronghold in Diyala province, north-east of Baghdad.

Further north the jihadists are also on the retreat. American commanders say that air strikes combined with a ground offensive by Iraqi Kurdish forces have pushed back IS from their positions west of Mosul, Iraq’s second-biggest city, which fell to jihadists last June. IS supply routes from its territory in Syria are being cut. Talk of an early summer assault on Mosul has also resumed. That seems premature. Efforts to rebuild the Iraqi army are unlikely to bear fruit so quickly. And the city could not be taken without a heavy toll in civilian lives.

The coalition is also having some success in hitting IS in its wallet. By destroying oil installations, the air strikes have denied IS its main source of cash. Oil receipts may have dropped by two-thirds to $750,000-$1.3m a day from $2-3m in June. Banks in areas under IS control may have run out of cash. IS is killing rather than ransoming hostages, having raised at least $20m in 2014. “The key thing is these sources of financing aren’t renewable,” says Matthew Levitt of the Washington Institute for Near East Policy, a think-tank. “While IS is a rich terror group, it is a poor state.” People in Raqqa, IS’s Syrian headquarters, say salaries are still being paid, but services—crucial to IS’s claim to rule—are drying up.

These setbacks may help explain the group’s turn to ever more ghoulish acts to bolster morale and keep up the flow of new recruits. That suggests an opportunity, says Mr Levitt. Stories are emerging of IS fighters who are killed or jailed by the group when they try to leave it, but they are not widely circulated. “We need [videos of] foreign fighters who have returned saying: ‘I went but was cleaning toilets;’...‘I went and wanted to leave and they killed my two brothers’,” says Mr Levitt. A long war needs not just guns and planes but also a comprehensive strategy and the patient waging of a battle of ideas.