The goals that animate the renewed U.S. bombing campaign in Iraq are a muddle. Any rationale for bombing Sunni militants there today suggests a prolonged campaign against them. Any effort we make against Sunni insurgents in Iraq contradicts our pro-insurgency policy in Syria. And while President Obama claims fidelity to the hope of making Iraq a stable multi-ethnic state, by defending Iraq’s Shi’ite regime and Kurdish North against Sunnis, the bombing may hasten Iraq’s dissolution.

The president’s stated goals are clear enough. Last night, he said that the airstrikes have two aims. First, they will protect Americans—several dozen diplomats and military personnel are apparently in Erbil, which is threatened by the recent advances of the Islamic State in Iraq and Syria (ISIS). Second, the president said that the strikes will defend civilians from the Yazidi minority. Tens of thousands of them are said to be encircled by ISIS militants. According to the president, U.S. aircraft will both drop supplies to the Yazidi and attack ISIS positions to break the siege.

The first goal doesn’t require bombing. If we are simply concerned about the well-being of U.S. personnel in Erbil, we would evacuate them. But they are there largely to help Iraqis fight ISIS in the first place. Seemingly, we are after some broader objective. Protecting the Yazidi from starvation and slaughter makes sense. But that objective can easily slide into broader ones.

As President Obama more or less said, the humanitarian danger in Iraq comes mostly from the success of ISIS and more broadly from the civil war. Getting the Yazidi to safety will not end the danger to civilians in Iraq. The logic that compels us to stop ISIS’s advance today seems likely to suggest bombing it continually. If ISIS is our problem, we are probably on the wrong side of the Syrian civil war.

The conventional wisdom in Washington is that we should aide moderate opponents of Bashir al-Assad’s government. But aiding any rebels there hurts the main Syrian force going after ISIS. We cannot foster insurgency in Syria and suppress one Iraq without contradiction. The president says that the bombing in Iraq falls under the “broader strategy that empowers Iraqis to confront this crisis” by creating a “new government that represents the legitimate interests of all Iraqis.” He promises increased U.S. support once a new government forms. The implicit message is that if the next Iraqi government has someone other than Nouri al-Maliki heading it and takes steps to deal with Sunni grievances, more support will flow. But bombing ISIS might increase Maliki’s or some other Shi’ite leader’s security, reducing their incentive to give ground to Sunnis.

If it’s stability in Iraq we are after, however, unity may be the problem, not the solution. Keep in mind that the United States has long gone along with near independence for the Kurds. Is there a greater increment of autonomy that would placate the Sunnis? Might Iraq’s stability and its unity be contradictory goals?

Responsible policymaking requires choosing among competing objectives. President Obama was right to get out of Iraq, but it is irresponsible to insist that we sacrificed nothing in doing so. The United States has been bombing Iraq on and off for more than two decades, each time with our leaders insisting a bit more force will do the trick. We ought to admit the impossibility of producing a satisfying result, tragic as that may be.