One practical consideration is that Maliki has aggregated so much direct control over his most competent military units that replacing him would disrupt the chain of command. The state institutions simply aren’t strong enough for a smooth transition of power: in a country where the prime minister often literally issues orders to generals via text message, it’s not just a matter of Maliki handing over his cell phones.

Given all of this, Iran is apparently disinclined to foment a political rebellion against Maliki among the Shia. Obama seems keenly aware of this dynamic. “Iran can play a constructive role if it is helping to send the same message to the Iraqi government that we’re sending, which is that Iraq only holds together if it’s inclusive,” he said. “If Iran is coming in solely as an armed force on behalf of the Shia and if it is framed in that fashion, then that probably worsens the situation.” The question is how to prevent the latter and induce the former.

To this end, U.S. military power could be a decisive lever. For all of the military help Tehran is willing to provide Baghdad, it still cannot match American air power. And only American planes can really exploit another major weakness of ISIS: its ambition to hold territory. For Iraqi and Iranian ground forces, the prospect of a land war looks intimidating because insurgents have accumulated a fleet of armored vehicles and an arsenal of heavy weapons. For an American fighter pilot, however, ISIS convoys and fortifications look like great things to bomb.