BARACK OBAMA has struck the jihadists in Iraq and—even if the action was belated and modest—he has so far been successful. But the Islamic State (IS) needs to be thwarted, so he must strike it in Syria, too. And that will prove much harder.

In Iraq the advance of fanatics bent on devastation has, for now, been halted (see article). The Yazidi minority which fled up a mountain near Sinjar in the north has mostly been saved. Iraq’s Kurdish region, the only reasonably governed part, is no longer in imminent danger. The great dam that threatens to inundate Mosul, Iraq’s second city, captured by IS in June, has been secured for the government by a combination of American air power and Iraqi and Kurdish ground forces.

Meanwhile, Iraqi politics has taken a welcome turn with the forcing out, after eight disastrous years, of Nuri al-Maliki, the sectarian Shia prime minister. By keeping Iraqi Sunnis out of his ruling circle and packing the senior posts in the army and security service with fellow Shias, Mr Maliki drove moderate Sunnis into the arms of the extremists. With luck, his designated replacement, Haider al-Abadi, will form a government that embraces a much fuller range of Iraqis.

But the jihadist threat is far from over. Innocents are still being murdered. On August 19th a British-accented IS jihadist beheaded an American journalist in revenge for Mr Obama’s air raids. IS still controls a third of both of the countries that featured in its former name, the Islamic State of Iraq and Greater Syria. It scorns national borders in its quest for a global caliphate. And it is attracting young Muslims abroad, some of whom will target their own countries. In short, it is a menace to the region and the world.

Striking IS in Iraq is only half the answer. If it is driven out, its fighters will regroup in Syria only to hit back later. That is why IS must be clobbered in Syria as well as in Iraq.

Mr Obama should now do what he ought to have done all along: give a decent supply of arms to Syria’s moderate rebels, who are equally menaced by IS. But even with weapons and money from outside, the moderates will not be able to dent IS. That needs aerial attack from America and its NATO allies.

This raises awkward questions. The internationally recognised governments of federal Iraq and of Iraqi Kurdistan begged Mr Obama to intervene. But bombing the jihadists in Syria is a different matter. Mr Obama will be accused of acting illegally and of aiding the government of Bashar Assad by attacking his mortal foes. Mr Assad, for his part, will mock that the West has belatedly acknowledged that he is the last bastion of defence against everyone’s real enemy.

Jaw jaw and war war

Mr Obama does not need the permission of Mr Assad. America does not recognise his regime; it has long called for him to be overthrown. Yet America can blunt his mockery and strengthen the anti-IS cause by raising the bombing of IS in Syria at the UN Security Council. A remarkably wide range of countries, including Egypt, Saudi Arabia, Iran and Turkey, the region’s biggest actors, see IS as a threat and agree that it must be defeated, not just contained. Many of those countries should not just back the mission, but join it. Russia, Mr Assad’s sponsor, has an eye on its own jihadists in the Caucasus and has long argued that the danger is extreme Islam. For it to vote to shelter IS would be bizarre—and revealing of Russian nihilism.

If Mr Obama is rebuffed in the Security Council, or if Russia holds out for an unacceptable shift in America’s policy towards Mr Assad, he should nevertheless go ahead and hit IS on both sides of the border. IS is too dangerous to be allowed to gain ground while the rest of the world stands by.