IT SOUNDS far-fetched but it may be true. A group of Irish peacemongers, from both sides of their long-divided island, claims to have made rare progress last month towards getting Arab and Kurdish Iraqis to settle their differences, which have been threatening to drag the country back to the level of bloodshed that engulfed it three years ago. With a South African who had helped reconcile white and black South Africans looking on, a clutch of Iraqi members of parliament got to unusual grips with the mechanics of sharing power between Kurds, Arabs and Turkomans in the disputed region of Kirkuk. If they can build on this momentum after the general election that is now expected in mid-February (the January date having slipped), a modicum of federal harmony may eventually be achieved—to the benefit of all Iraqis.

One suggestion that may be taken up is the creation, at least for a time, of mixed councils to run the province. Another fruitful idea is to set up a permanent framework for talks involving the outside backers of the various Iraqi communities. For London, Boston and Dublin read Baghdad, Ankara (Turkey's capital) and Erbil, Iraq's Kurdish one.

The latest meeting was sponsored by one of Iraq's two vice-presidents, Adel Abdel Mahdi, a Shia Arab sometimes mooted as a possible next prime minister. More such gatherings are expected. Other efforts to solve the Kirkuk puzzle have intensified, under the aegis of both the Americans and the United Nations.

On November 22nd units of the Iraqi federal police and the Kurds' gendarmes, known as the Zeravani, trained publicly together for the first time. It is hoped that this month tripartite patrols around Kirkuk will start, with government and Kurdish troops to be overseen by American ones.

Meanwhile, staff at the UN mission in Baghdad are drawing up lists of possible concessions that might mollify all sides. In parliament there is talk of a dialogue council to resolve land disputes, determine the role of the Kurds' military forces (known as the Peshmerga), share out oil revenues, settle Kurdistan's constitutional status and agree on the voters' register.

This surge in activity has come not a moment too soon. Tension over Kirkuk has been worsening. Although the rest of Iraq has been a lot quieter, violence along the Arab-Kurdish border (the “trigger line”) has been rising. At a rate of about 130 attacks a month, more violence is taking place there than in the rest of Iraq put together. Moreover, Arab-Kurdish tension has been gumming up politics in Baghdad.

And time is running out. By next summer, most American forces, who have been Kirkuk's ultimate peacekeepers, will have gone. Those left may no longer have the strength to put out fires. Yet an opportunity may beckon. After next year's general election, Iraq's politicians will haggle over the make-up and programme of the next government, possibly for as long as four or five months. Dealing with Kirkuk could be part of any bargain. Most outsiders closely involved in Kirkuk have long argued that it cannot be solved piecemeal but only as part of a big package.

Most of Iraq's non-Kurds—Shia and Sunni Arabs and Turkomans (kin of the Ottoman Turks who for centuries ruled what is now Iraq)—fiercely oppose what they consider to be the Kurds' excessive demands, especially their desire to control Kirkuk. Arab and Turkoman leaders in Kirkuk recently formed an electoral front to counter the Kurds' numerical advantage since they took back the province in the wake of Saddam Hussein's overthrow by the Americans in 2003. The Arabs and Turkomans insist that the city, now reckoned to contain some 850,000 people, should never be part of an autonomous Kurdish region. Few other issues unite non-Kurds so passionately. An Iraqi prime minister who gave away the city would almost certainly lose his job. Iraq's neighbours too, especially Turkey but also Iran, vehemently object to the idea of the Kurds controlling Kirkuk, lest it boost Kurdish separatism in their own backyards.

Yet the Kurds are equally adamant. They call Kirkuk their Jerusalem. Their politicians in Erbil may have become even more inflexible since the long-dominant parties lost ground in a regional election this summer to a new group called Goran (Change) that beats the nationalist drum while inveighing against corruption. Masoud Barzani, the region's president, and Jalal Talabani, Iraq's president, who runs one of the two main Kurdish parties, have raised the rhetorical heat over Kirkuk.

The Kurds have a strong moral claim to the province. During two decades of enforced Arabisation under Saddam, some 250,000 Kurdish residents of Kirkuk were expelled. Few Arab leaders acknowledge the brutality of that crime. If they did so, a compromise might be easier. The Kurds might, for instance, at least consider an Iraqi government proposal to create a city council with seats split equally three ways for a limited period (to be precise, 32% for each of the three main groups and 4% for the tiniest minorities, such as Christians). “It would give all sides time to get used to a situation where nobody is a clear winner,” says Iyad al-Samarraie, a Sunni Arab who is the parliament's speaker in Baghdad.

The Irish peacemakers have suggested, among other things, a detailed “road map” towards sharing power that could lead to a multiethnic administration. Though understood to be only temporary, such a system, optimists hope, would gradually become entrenched.

But the Kurds would have to give up their ambition to make Kirkuk an immediate and integral part of an autonomous Kurdistan. That suggestion would outrage them. The city of Kirkuk was once predominantly Kurdish. They have shed much blood losing it and in seeking to get it back. But the alternative—a war with the Arabs that might draw in neighbouring countries—would almost certainly see the Kurds lose in the long run, even though they are better armed than ever before.

A parting gift from Mr Obama

The Americans are the only ones who might persuade the Kurds to change their mind. American representatives in Baghdad have become impatient with the Kurds, considering them to have overreached themselves in recent years. “But nobody on the American side has ever looked Barzani in the eye and said, ‘You can't have Kirkuk',” says a Western diplomat. In the past the Americans were sympathetic to the Kurds. But now their patience is wearing thin.

The American vice-president, Joe Biden, who is Barack Obama's point man on Iraq, may urge Mr Barzani after the Iraqi election to say goodbye to a Kirkuk controlled solely by the Kurds. It may be suggested that the province should—at least temporarily—have a special status. In return for giving up soil, the Kurds could—as part of a quid pro quo—get a better deal on the oil in their territory.

Would Mr Barzani listen? The Kurds need America's patronage more than ever now that its troops are leaving and the Kurds' opponents in Baghdad have a freer rein. It may be the last bit of really tricky diplomacy in Iraq that falls to America.