Times journalists are in Iraq’s Sunni heartland to evaluate rebuilding efforts after battles with the Islamic State.

FALLUJA, Iraq — Iraqi forces had taken Falluja from the Islamic State months before, and Sabah Rashid was more than ready to return home. But the police warned him not to go.

Fleeing Islamic State fighters had rigged bombs all through his south Falluja neighborhood, and these had still not been cleared, they told him. Insurgent corpses were said to lay unrecovered.

Mr. Rashid, 30, a determined sort, moved back into his ransacked house anyway — he and his family fled the Islamic State three years ago and did not want to wait. Last week, they were camped out in their sagging house with no heat, electricity or running water. They boiled water on a wood fire. And they waited with mounting frustration for promised government aid.