This article first appeared on Foreign Policy.

The Islamic State of Iraq and al-Sham (ISIS) has been the focus of most media attention since its series of military victories in Iraq, but it is not the greatest threat to the Iraqi state. Rather, the success of the organization, which recently declared a new caliphate and rebranded itself as the Islamic State, is a symptom of a deeper problem that has been simmering since the U.S. invasion in 2003: the unresolved issue of the Sunni Arab community's future in Iraq. Most of Iraq's Sunni Arabs don't support the ISIS caliphate -- but they do want a new, different government in Baghdad.

In the assault that seized vast stretches of Iraqi territory in the past month, the Islamic State was the public face of a broader Sunni Arab coalition rising up against the central government and its forces, which had been harassing Sunni inhabitants of towns and cities like Mosul and Tikrit.

Many of those fighting alongside the Islamic State come from the Army of the Men of the Naqshbandi Order, a mix of Muslim mystics and loyalists to Saddam's vice president, Izzat Ibrahim al-Douri, who evaded capture after the U.S. invasion. Connected to Douri's fighters is a virulently anti-Shiite group of clerics called the Muslim Scholars Council, led by Harith al-Dari and his son Muthanna, clerics who worked with Saddam out of Baghdad's Umm al-Qura Mosque -- the one with minarets designed to look like AK-47s. Another group in the Sunni Arab uprising is the Islamic Army, comprised of former officers and soldiers of Saddam Hussein's Baath Party -- an "army" that is not Islamic at all but seeks a religious cover for legitimacy rather than depending on that of the Saddam regime.

The revolt across western Iraq is more than just former regime dead-enders. Tribal elements -- including many who once fought against ISIS's parent organization, al Qaeda in Iraq -- have joined the broader Sunni revolt against government forces. Figures such as Sheikh Ali Hatem al-Suleiman, a prominent tribal leader in the western Anbar province, have declined to fight the Islamic State until Prime Minister Nouri al-Maliki steps down.

In Baghdad, much of the Sunni Arab political class also opposes Maliki, including the largely white-collar Muslim Brotherhood and wealthy businessmen like Osama and Atheel al-Nujaifi -- the former speaker of parliament and the former governor of Mosul, respectively.

If these disparate elements of Iraq's Sunni Arab community don't share Baghdadi's goal of a caliphate, then what do they want?

None of these Sunni groups have expressed any support for the Islamic State's self-styled "caliph," Abu Bakr al-Baghdadi. Indeed, to them his caliphate is an abomination. The group's determination to impose its rules on modern society alienated Syrians, and is likely to do the same in Iraq. In Syria, the Islamic State's brutal enforcement of its vision of Islamic norms and its labeling of those who disagreed as apostates eventually led groups like the Free Syrian Army and even the al Qaeda-linked Nusra Front to launch war against it. So far, the Islamic State in Iraq has tread more lightly, but it's not clear this will last. It has already issued a code of proper conduct for Mosul -- a possible harbinger of future conflict with the other Sunni Arabs.

There have, in fact, already been clashes between these jihadists and the old regime loyalists of the Islamic Army and the Naqshbandi in Mosul and in Diyala, northeast of Baghdad. Some tribal leaders, with clear memories of al Qaeda's past brutality, have also announced that they reject the Islamic State's ideological vision, and could come to blows again.

If these disparate elements of Iraq's Sunni Arab community don't share Baghdadi's goal of a caliphate, then what do they want? The Iraqi Sunni Arabs are a diverse group so, not surprisingly, they don't all agree.

Douri and his allies in the Muslim Scholars Council seek the overthrow of the existing state and a return of the old Sunni Arab-dominated Iraq under new management. By contrast, some of the tribal sheiks and the Baathists in the Islamic Army speak of removing Maliki and supporting a broad, new central government in Baghdad that includes genuine representation of the Sunni Arabs.

In a reversal of their thinking after 2003, many Sunni Arabs also now call for a Sunni Arab region modeled off the Kurdistan Regional Government that they so bitterly opposed 10 years ago, during the drafting of the present Iraqi constitution. The present constitution would allow a Sunni Arab regional government with its own security forces and a wide margin of self-rule. They are surely also thinking about the share of Iraq's big oil revenues from southern and northeastern Iraq that would go to their region, which would be centered in western Iraq.

This suggests that there is space to negotiate with at least some of the Sunni Arabs. These figures would likely be willing to stop the fight against Baghdad in return for a reformed central government and an agreed path to decide if and where to establish another regional government in Iraq. However, it is impossible to overstate the fears and suspicions of all sides -- Shiites, Kurds, and Sunni Arabs -- over past behaviors and excesses. Iraqi political deals usually require lots of negotiation, and this time promises to be no different.

If we hope to avoid a wider conflict across the Middle East, much depends on Iraq's Sunni Arab and Shiite communities finding a way to live together.

Many thorny issues would no doubt complicate any such deal. In several of the provinces where the Sunni Arabs would likely want their regional government, there are towns that are primarily Shiite or Kurdish. Would they fall under a Sunni Arab regional government? How would oil revenues be shared with a new Sunni Arab region, and how would its local security forces be organized? What role would the Sunni Arab military cadres have in the national security forces? As any deal could set precedents for a future Shiite region, the talks would be arduous and could delay announcement of a new government.

Perhaps the most important question is how the Sunni Arabs would confront the Islamic State, which is now anchored between the city of Raqqa in central Syria and Mosul in Iraq. In Syria, after several years of uneasy coexistence, the more moderate elements of the armed opposition -- such as the Free Syrian Army, the Syrian Revolutionaries Front, and Jaysh al-Mujahideen --finally turned on the Islamic State and are now in an existential fight. It is hard to see how Iraq's Sunni Arabs could ever join a deal with a new central government in Baghdad without also confronting the jihadists within their midst.

President Barack Obama's administration rightly insists that combating the Islamic State above all requires a political settlement among the Iraqis. A political deal will be difficult to achieve, but it may be possible. If we hope to avoid a wider conflict across the Middle East, much depends on Iraq's Sunni Arab and Shiite communities finding a way to live together.

This article first appeared on Foreign Policy.

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