Baghdad called President Obama’s bluff and he came through. He had refused to provide air support to Iraqi government forces until the Iraqis got rid of their divisive sectarian prime minister.

They did. He responded.

With the support of U.S. airstrikes, Iraqi and Kurdish forces have retaken the Mosul dam. Previous strikes had relieved the siege of Mount Sinjar and helped the Kurds retake two strategic towns that had opened the road to a possible Islamic State assault on Irbil, the capital of Kurdistan. In following through, Obama demonstrated three things: the effectiveness of even limited U.S. power, the vulnerability of the Islamic State and, crucially, his own seriousness, however tentative.

The last of these is the most important. Obama had said that there is no American military solution to the conflict. This may be true, but there is a local military solution. And that solution requires U.S. air support.

It can work. The Islamic State is overstretched. It’s a thin force of perhaps 15,000 trying to control a territory four times the size of Israel. Its supply lines are not just extended but exposed and highly vulnerable to air power.

Stopping the Islamic State’s momentum creates a major shift in psychology. Guerrilla armies thrive on a sense of inevitability. The Islamic State has grown in size, demoralized its enemies and attracted recruits from all over the world because it seemed unstoppable, a real caliphate in the making.

People follow the strong horse over the weak horse, taught Osama bin Laden. These jihadis came out of nowhere and shocked the world by capturing Mosul, Tikrit and the approaches to Kurdistan, heretofore assumed to be impregnable.

Now that’s begun to be reversed.

Obama was slow to bring American power to bear. And slower still to arm the Kurds. But he was right to wait until Baghdad had gotten rid of Nouri al-Maliki, lest the U.S. serve as a Shiite air force. We don’t know how successful Haider al-Abadi will be in forming a more national government. But Obama has for now wisely taken advantage of the Abadi opening.

The problem is that the new policy has outgrown the rationale. Our reason for returning to Iraq, explained Obama, is twofold: preventing genocide and protecting U.S. personnel.

According to Obama’s own assertions, however, the recent Kurdish/Iraqi advances have averted the threat of genocide. As for the threat to U.S. personnel at the consulate in Irbil, it too is reduced. It was a flimsy rationale to begin with. To protect Americans in an outpost, you don’t need an air war. A simple evacuation would do.

Besides, what does the recapture of the Mosul dam, the most significant gain thus far, have to do with either rationale? There are no Christians or Yazidis sheltering there. Nor any American diplomats. So Obama tried this: If the dam is breached, the wall of water could swamp our embassy in Baghdad.

Quite a reach. An air war to prevent flooding at an embassy 200 miles downstream? Well yes, but why not say the real reason? Everyone knows it: The dam is a priceless strategic asset, possession of which alters the balance of power in this war.

And why not state the real objective of the U.S. air campaign? Stopping, containing, degrading the Islamic State.

These are the worst people on earth. They openly, proudly crucify enemies, enslave women and murder men en masse. These are not the usual bad guys out for land, plunder or power. These are primitive cultists who celebrate slaughter, glory in bloodlust and slit the throats of innocents as a kind of sacrament.

We have now seen what air cover for Kurdish/Iraqi boots on the ground can achieve. But for a serious rollback campaign, Obama will need public support. He has to explain the stakes and the larger strategy.

“People like this ultimately fail,” Obama said of James Foley’s murderers. Perhaps. But “ultimately” can be a long way – and thousands of dead – away. The role of a great power, as Churchill and Roosevelt understood, is to bring that day closer.

Charles Krauthammer is a columnist for the Washington Post. He can be reached at:

letters@charleskrauthammer.com