Only Assad’s Syria and Iran can and would provide plausible ground forces in short order. Turkey, the other possible partner, has shown itself to be more interested in checking its own Kurdish population than in fighting ISIS abroad. On paper, Assad’s army numbers over 100,000, and his air force contains around 300 jets. Even if his actual fighting force is half that, Syria’s is still the best positioned and most usable outfit among the neighboring Arab states. Iran’s forces are even more potent.

Mr. Assad has thus far proved cagey. He hasn’t made the defeat of ISIS his top priority. He remains zeroed in on the rebels, while brokering his own stolen oil internationally on behalf of the ISIS jihadis who took it. Recently, however, Assad has been signaling that he sees things differently, but he won’t turn his attention fully to ISIS without quiet assurances from the Americans—and probably the Russians, too—that this won’t disadvantage him against the rebels. Russia, brimming with unhappy, armed Muslims, is even more threatened by the existence of ISIS than the United States. Moscow could help facilitate cooperation between Syria, Iran and the U.S., not because Mr. Putin is kind hearted, but because it is in his obvious interest.

Cooperating with Assad is also the only feasible way, at present, to lessen the humanitarian nightmare in Syria.