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(economist.com) The killing on November 12th of Mohammed Emwazi, the Islamic State (IS) video executioner dubbed “Jihadi John”, has dominated the headlines and prompted David Cameron, the British prime minister, to warn jihadists: “We have a long reach, we have unwavering determination and we never forget about our citizens.” But probably of far greater significance for the fight against IS was the recapture of the town of Sinjar in north-west Iraq by Kurdish Peshmerga fighters, and the start of an offensive by Iraqi security forces to expel IS from Ramadi, the capital of Anbar province.

Emwazi’s death—the result of a strike by an American drone on a “tactical unit” in the IS stronghold of Raqqa—was confirmed as “99% sure” by American military sources. A British citizen, Emwazi became the symbol of IS brutality last year through carefully staged propaganda videos showing the beheading of hostages from Britain, America and Japan. The successful targeting of such a high-profile figure will give a boost—mostly symbolic, but also raising questions about IS’s internal security—to a campaign against the jihadists that appeared to be flagging, especially since Russia began air strikes against rebel groups in early October. Of late, America has stepped up its air strikes against oil facilities that IS controls in eastern Syria in an attempt to disrupt one of its sources of funds.

If the situation in Syria remains extraordinarily confused, there are increasing signs of some progress against IS in Iraq, which is where its main strength lies. The assault on Sinjar by the Peshmerga, backed up by concerted coalition air strikes over several days, began in earnest earlier this week. IS forces reportedly pulled out of the town after two days of intense fighting, allowing the Peshmerga to walk in virtually unopposed on November 12th.

The strategic importance of the Kurdish victory could be considerable. It should pave the way to cutting off supply lines between Raqqa and IS-held Mosul, Iraq’s second-biggest city with a population (at least before the arrival of IS in June last year) of 1.5m. The retaking of Mosul remains the most ambitious medium-term objective of the Iraqi government and the American-led coalition. IS has well-prepared defensive positions around the city, but the morale of its fighters will suffer as the effects of isolation intensify.

Correspondingly, the taking of Sinjar will have given a major boost to the Peshmerga and strengthened the argument for supplying them with heavy weapons, something the Shia-dominated government in Baghdad has resisted. They may need them if they are to hold on to Sinjar as IS still controls Baaj, 20 miles to the south, and Tal Afar, 30 miles to the east. Both are mainly Arab towns that may have to be retaken by Iraqi security forces rather than by the Peshmerga.

When that might happen will depend on the progress made in Ramadi. A few weeks ago Iraqi forces, supported by coalition air power, managed largely to encircle the city of 450,000 people, which shockingly fell to IS in May. But the start of an attempt to liberate the city has been delayed by heavy rain and the need to clear the first lines of IS booby-traps. Another reason for the delays may be caution: a failure to retake Ramadi would be a terrible setback to the beleaguered government of Haider al-Abadi. It badly needs to show that the Iraqi army is recovering some of its fighting capacity after its dreadful showing over much of the past 18 months. A successful attack would indicate that the government is not wholly dependent on Iranian-backed Shia militias in the struggle against IS.

More than anything, a succession of defeats for IS should help puncture the image of invincibility that has been so vital to the ability of the “caliphate” to recruit fighters and terrorise people in the towns it controls into submission. Liberating Sinjar and Ramadi is not the beginning of the end, but, if achieved, could at least mark the end of the beginning.