Iraq was often a black-and-white place for the Bush administration loyalists who served in the American occupation government. Ensconced in Baghdad’s heavily fortified Green Zone, they spent more time interacting with fellow Americans than Iraqis. Still, they were convinced that they knew what was best for Iraq. The old Iraqi Army, for instance, was bad. Exiled political leaders were good. Members of the Baath Party were, of course, in the bad column. Outside the Green Zone’s 17-foot-high walls, America’s military leaders saw a more sepia-toned landscape. It was not black and white, just hazy shades of brown.

The relationship between soldiers and the civilians in charge of reconstruction had faltered in the aftermath of previous U.S. military operations in Haiti, Kosovo, and Somalia. Iraq, however, was supposed to be different. It was supposed to be a chance to get military-civilian cooperation right. But, from the start, policies concocted by the U.S. Coalition Provisional Authority (CPA), headquartered inside Saddam’s marble-walled Republican Palace, rarely played out on the ground as CPA leader Ambassador L. Paul Bremer III and his subordinates expected. Bremer’s first official act upon arriving in Baghdad was to fire tens of thousands of Baathists from their government jobs. But what about the 15,000 teachers that included? What about the top managers at the Ministry of Health? Or the hundreds of old soldiers who had been made honorary senior members of the party after spending years in Iranian prisoner-of-war camps?

Those working for the CPA—many of whom were young civilians politically loyal to the Bush administration—didn’t grasp these nuances, or the need for pragmatic exceptions to their neoconservative edicts. But many in the military did. In the northern city of Mosul, for...