A more potent partner would be the world’s only other Shia government, that of Iran. This prospect drives some prominent Washington hawks crazy. While they would like to defeat ISIL, they don’t want to do so at all costs. They fear that a successful cooperation with Iran could leave that country with greater regional power, which might well be true. In their view, it is better to tolerate ISIL than destroy it in a way that could produce benefits for Iran.

Anti-ISIL Sunni tribes in the conflict zone are logical allies, but they clearly cannot turn this tide alone. Nor can our Kurdish friends. The government of Iraq is a logical partner — its government is Shia-dominated, and ISIL wants to slaughter all Shias — but it is weak and divided.

One way to fight ISIL would be to look around the Middle East, ask “Who really wants to help us crush these guys?” and accept all who raise their hands. Instead we have decided to be oddly picky about our allies. As long as that remains our policy, we fight this war with one hand tied behind our back.

Ramping up our military response — say, by using shock-and-awe carpet bombing instead of isolated strikes by warplanes or drones — would not significantly improve prospects for wiping out ISIL and might well result in a slaughter of innocents that would attract new sympathy to its cause. A far better tack would be to intensify our coalition building. This we refuse to do, however, because we fear the implications of joining with other anti-ISIL forces.

How seriously the United States and its putative friends should take the threat from the Islamic State of Iraq and the Levant (ISIL) is debatable. So is the question of how we should respond to that threat. One thing, however, is eminently clear: The loose, slowly emerging anti-ISIL coalition is not using all the weapons at its disposal.

It is wrong for the Obama administration to suggest that we are using all our political and diplomatic resources in the fight against ISIL.

“The Iranian regime is seeking to lure Washington into cooperation in Iraq,” Gen. Hugh Shelton, a former chairman of the Joint Chiefs of Staff, warned recently. “Washington must not fall into that trap.” No less a figure than former Secretary of State Henry Kissinger has asserted, “I consider Iran a bigger problem” than ISIL. Secretary of State John Kerry has agreed that cooperating with Iran “would not be right for any number of reasons,” though he appeared to keep the door ajar by saying the possibility could be discussed “through a process which we are entirely prepared, over a period of time, to engage in.”

The United States shows less concern about its other allies. The White House has enlisted some highly dubious partners for its fight against ISIL. They include Gulf states that have financed Sunni extremist groups for decades, as well as Turkey, which has allowed streams of militants to enter Syria through its territory and tolerates a cross-border oil trade that helps ISIL finance its incipient caliphate. Yet we cannot bring ourselves to work with Iran or Shia militias in Iraq, Lebanon and Syria that have a life-or-death interest in this conflict.

Nor dare we even consider the possibility of partnering with Syrian forces tied to the bloodstained regime of Bashar al-Assad. We apparently don’t detest ISIL enough to work with such reprehensible partners.

By pointedly excluding Iran from a meeting in Paris on Monday aimed at shaping anti-ISIL strategy, the U.S. not only intensified hostility between it and Iran but also showed how limited its desire to crush ISIL really is. This approach brings to mind the cliché that warns against cutting off one’s nose to spite one’s face.

The idea that Iran is more dangerous to the United States and the West than ISIL is deeply mistaken, for two reasons. First, Iran shares a fundamental outlook with the U.S.: that sovereign states must rule the world, that every inch of territory on earth must be under the control of a state and that ungoverned areas are always dangerous. Second, it is clearly possible to imagine changes in Iran that would allow eventual reconciliation with Washington. No such reconciliation will ever be possible with ISIL.

The question of working with Assad is more difficult. It remains the official policy of the United States that he must go, and the savagery with which he has helped destroy his own country marks him as one of the modern world’s most odious tyrants.

Yet the U.S. managed to partner with Joseph Stalin, the murderer of millions, to win World War II, because America decided to defeat Nazism at all costs — even the moral and political cost of allying with a monster. We have not made such a decision about ISIL. Although we wish to see it destroyed, our wish is not strong enough to displace other regional goals.

Whether the fight against ISIL is so important that we should collaborate with unsavory partners is a legitimate question. It is wrong, however, for Barack Obama’s administration to suggest that we are using all our political and diplomatic resources in this fight. Neither the U.S. nor any other country is truly waging all-out war against ISIL. We are fighting half-heartedly. To pretend otherwise is misleading propaganda.