AP Photo

A scorching summer heat is settling on Baghdad. The streets are calm and traffic flows, slowed only by the multiple checkpoints, especially near bridges and government buildings. Given that the policemen on duty carry out only a cursory glance at vehicles and their passengers, it is perhaps surprising there haven’t been more frequent bombings in recent weeks. (The last series of bomb attacks across Iraq, on May 10, left at least a hundred dead.)

To security officials, the relative quiet suggests that many former insurgents and their supporters—including some Sunnis who in the past rejected the political process—have been biding their time. Having decided to participate in the March 7 parliamentary elections, they have been inclined to let the...