FALLUJAH: The Iraq Victory That Could Lose the War.

For now, the Iraqi government has buoyed its chances at short-term survival by more or less ending ISIS’s presence in Fallujah, which Baghdad’s politicians connected to a series of bombings in Sadr City that harmed the Iraqi government’s reputation for providing security.

Even so, the Shia militias’ military autonomy and sectarian abuses in addition to the Iraqi Security Forces’ tacit cooperation with them to enter Fallujah should raise serious concerns in Baghdad and Washington.

“Obviously, the Shia militias’ offensive against Fallujah complicates things in important ways,” Kenneth Pollack, a senior fellow at the Brookings Institution and former CIA intelligence analyst, said in an email. “They don’t fully respond to the Iraqi government. They frighten the Sunnis, largely because they have participated in ethnic cleansing.”

The long-awaited effort to retake Mosul was put on hold to retake Fallujah instead — almost certainly to please Iran. That the offensive has bolstered Tehran-backed Shia militias is a feature, not a bug.