The governments of Iran and Syria may be opposed the Levantine militant group that calls itself the Islamic State but they are hardly allies in the fight against it. Rather, they helped create the problem in the first place.

As the United States steps up its involvement in the war against the Islamic State, not only in Iraq but in neighboring Syria as well where President Barack Obama had been so reluctant to commit American forces, Bashar al-Assad’s ruthless regime in Damascus and the brutal theocracy that sits in Tehran might seem natural allies. Both oppose the revivalist version of Sunni Islam that is espoused by the Islamic State — Assad because he is secular and battling Sunni fanatics in his own country; Iran because it is Shia and fears losing a proxy in Baghdad.

The case for clandestinely teaming up with both regimes could even be strengthened by pointing to the unwillingness of America’s allies in the region to commit to the fight. Jordan and Saudi Arabia allow some training of supposedly moderate Syrian rebels to take place on their soil. The monarchies in the Persian Gulf will gladly funnel money and weapons into Iraq and Syria. But they won’t commit their own soldiers, who were trained by Americans, or their own weapons, which the United States supplied.

Others are even culpable in the Islamic State’s rise. Nominal allies Qatar and Turkey foolishly backed the anti-Western, radical Sunni militants in Syria, perhaps calculating that deposing Assad was worth the prize of fomenting a “caliphate” on their doorsteps.

As several dozen Turkish nationals are still held hostage by fighters of the Islamic State in Iraq, three months after they overrun the city of Mosul and captured the Turkish consulate there, surely the grand strategists in Ankara must be regretting the choices they made? And yet they refuse to support their NATO ally America to push back the Islamic State.

It’s not just Turkish strategists who seem to have forgotten who their enemies are, though. Proposals for an American entente with Iran and Syria against the Islamic State — previously known as the Islamic State of Iraq and Syria (ISIS) — are no less shortsighted. These two countries created the group — or at least the conditions under which an entity like it could emerge.

Assad deliberately stoked the sectarian flames in his country when an uprising against the regime erupted more than three years ago, focusing on suppressing Sunni dissent and portraying the insurrection as a terrorist movement, orchestrated by foreign enemies of the Syrian state. The most fanatic rebels were almost left alone in the desert northwest while Assad’s henchmen, including fighters from Lebanon’s Hezbollah, eradicated entire Sunni villages bordering the coastal heartland of his Alawite sect.

As Middle East expert Adam Garfinkle writes at The American Interest, Iran’s hegemonic exertions, including its support for both the Assad regime in Syria and radical Shia movements in Iraq, “have raised an existential threat to the Sunni Arab regimes and have radicalized heretofore mostly latent sectarian cleavages in the region.”

When the feeble Sunni Arab states proved feckless in responding, the radicalization process, with mischievous help from countries like Qatar as well as Turkey, created the monster that is ISIS. The point? It is not possible to extirpate ISIS unless we also address its source: Iranian power projection through Arab Shia militias (which, by the way, extends all the way to the Houtis in Yemen).

“That is why,” argues Garfinkle, “if the United States attacks ISIS in Syria, it must also attack Assad regime assets and, for good measure, those of Hezbollah as well.”

If it doesn’t, he warns, the Sunni Arabs the American hope to enlist as allies against the Islamic state are likely to conclude that the United States has secretly sided with Iran. “And a nuclear deal that can be interpreted as a win for Iran will mightily reinforce that perception.”

The enemies of America’s newest enemy in the Middle East are not its friends. Nor are they any less dangerous only because a seemingly crueler threat has emerged.