EVEN before America has properly put together its coalition to “degrade and ultimately destroy” Islamic State, the jihadist group that controls swathes of Iraq and Syria, it thinks it is making military progress. IS’s advance has already been halted, and the group has been pushed back on several fronts. IS can lose as well as win, say the Americans; triumphant convoys waving black flags down Iraqi streets should not expect to survive for long.

The diplomatic campaign against IS is making progress, too. On September 15th representatives from 27 countries converged on Paris (pictured above) to declare their backing for the Iraqi government’s bid to recapture all IS-controlled areas “by any means necessary, including appropriate military assistance”.

Iraqi officials delightedly reel off the names of countries that have pledged support: America has already plunged in; France has launched surveillance flights, with hints of deeper involvement (Britain, more quietly, is doing likewise); Belgium, where a Jewish museum was attacked by a seeming IS henchman, has signed on for the air campaign, as has Australia; Germany, Norway and Denmark have variously committed advisers and weapons to Iraq’s Kurdish region and the Iraqi government. Several Arab states, says John Kerry, America’s secretary of state, are prepared to take part in air strikes.

Barack Obama, the American president, is on track to secure congressional approval for plans to train and arm “moderate” rebels in Syria. But he appeared to disown a suggestion by his senior military chief that American soldiers could be embedded with Iraqi fighting units.

For America, the heart of the strategy is to turn disgruntled Sunnis against the jihadists, especially in Iraq. Having Sunni Arab rulers as allies helps, but the effort must start with reform in the Iraqi government. Though of the same stock as his heavily criticised predecessor, Nuri al-Maliki, Iraq’s new prime minister, Haider Abadi, speaks more convincingly of including Sunnis. Both men rose through the ranks of Dawa, a Shiite underground movement that fought the Iraqi dictator, Saddam Hussein. Mr Abadi has ordered a halt to air strikes in built-up areas (though an errant Iraqi bomb struck a hospital in the besieged Sunni city of Falluja, which IS has in effect controlled since January). He has suggested that Gulf states finance reconstruction of war-battered Sunni areas.

Iraq’s president, Fuad Masum, a Kurd, has suggested that four Sunni-majority northern provinces could merge into a Sunnistan bloc alongside Kurdistan. Under the constitution, he adds, it could draft its own National Guard, like the Kurdish peshmerga, without the approval of the Baghdad government. That said, despite the demand by Western and Gulf states for Mr Abadi to appoint Sunnis to senior cabinet posts, Iraq’s parliament on September 16th rejected his nominees for the defence and interior ministries.

Once bitten, Iraq’s Sunni Arab tribes are twice shy. In 2007-08, they worked with America to set up the Sahwa or “Sons of Iraq” militias, to fight IS’s precursor, al-Qaeda in Iraq, only for Mr Maliki to disband them once America left. Loyal today, caution some Iraqi officials, such fighters might yet switch sides and bolster IS’s capabilities. Critics point to the objections raised by some milder Sunni groups, including the Muslim Brotherhood, to renewed Western intervention in the region.

Indeed, one point of friction in the anti-IS coalition is the treatment of the Brotherhood: it is supported principally by Qatar and Turkey, and fiercely opposed by Saudi Arabia, the United Arab Emirates and Egypt, whose military government toppled the elected president from the Muslim Brotherhood, Muhammad Morsi. American officials say some allies had wanted the coalition to confront the Muslim Brotherhood as well as IS jihadists.

Not the Brothers’ keeper?

Qatar’s close links to the Brotherhood and vocal support for its varied branches have long irked neighbouring monarchs, and latterly Israel too. Qatar has abruptly changed its tune. At least seven senior Egyptian Brothers, exiled since the July 2013 coup, are to leave the emirate, most likely for Turkey. Qatar’s reconciliation with its neighbours will help military co-ordination: America’s main air and logistics base in the region happens to be there.

Winning support from Sunnis in and out of Iraq risks creating an opposite problem, stirring the suspicions of Shias, who form Iraq’s majority, and of Iran, a principal backer of the Iraqi government.

Iran and Syria (ruled by the Alawite sect, regarded as an offshoot of Shia Islam) were excluded from the Paris conference. Iraq’s new foreign minister, Ibrahim Jaafari, another Dawa man, brimmed with frustration at the absence of Iran. “No country has offered Iraq more support curbing IS’s advance,” seethed an Iranian official, meeting his Iraqi counterparts on the sidelines. “Had our men not intervened, IS would have swept into Baghdad.” One reason for America’s intervention was the fear that Iran and its Shia militia allies would extend their reach.

On Syria, Mr Abadi has quietly retreated from Mr Maliki’s vocal support for Bashar Assad’s regime. An estimated 20,000 Iraqi militiamen who helped defend Damascus, Mr Assad’s capital, have returned home to defend Baghdad. But Mr Abadi has stopped short of committing his country to neutrality in the Syria war as Iraq’s Sunni citizens and neighbours want him to do. His officials query the wisdom of co-ordinating the campaign against IS with Iraq’s government, but not Iran’s or Syria’s—positions reiterated by Russia. Anxious to keep his Russian guests in the conference room, François Hollande, the French president, tellingly emptied his speech of criticism of Mr Assad. Doubtless with a nod from Iran, varied Iraqi Shia militias whisper that IS is a CIA creation, and mutter that any Western intervention on the ground could be met by Shia resistance.

Deep suspicions also linger between the Baghdad government and Kurds, in spite of their temporary convergence of interests and the hurried Western effort to arm the Kurds to hold the line against IS.

Attempts to orchestrate the anti-IS coalition face other obstacles. Turkey, despite being a NATO member and sharing a porous stretch of its 900km (550-mile) Syrian border with IS, has shied from committing to any military role. It not only fears for the lives of 49 Turkish consular staff and family members held hostage since IS’s capture of Mosul, but also retaliatory terror attacks such as one that killed 52 people in the border town of Reyhanli last year. Officials suspect IS has planted sleeper cells. Others have similar worries: Australian police carried out several raids in Sydney and Brisbane this week after receiving intelligence that IS was urging sympathisers to behead a member of the public at random as a “demonstration killing”. Turkey also worries about the growing prowess in the fight against IS of Syrian Kurdish militias that are politically aligned with the PKK, a group that has fought a 30-year Kurdish insurgency inside Turkey.

Jordan, another front-line state through which supplies have flowed to Syrian rebels, is also wary of public commitment. Like Turkey, which may help by sealing its border more tightly to IS fighters and smuggled fuel, it will probably aid the coalition quietly. The flow of Western and Arab-supplied arms and trained fighters through Jordan has already made life more painful for Mr Assad’s regime, with non-IS rebel groups in southern Syria recently advancing to within 50km of Damascus.

In the short term, Mr Obama and his coalition may well be able to degrade IS. But destroying the group is a different matter altogether. It will require a long campaign which he will bequeath to his successor, and a sustained political effort to hold together the disparate coalition.