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Say what you want about Mahmoud Ahmadinejad, but “he knows how to work a room.” So claims Flynt Leverett, the contrarian Iran analyst who, with his wife Hillary Mann Leverett, paid a visit to the Iranian president in New York City last fall. During the sit-down at Manhattan’s InterContinental Barclay hotel with a group of invited academics, foreign policy professionals, and other Iranophiles, the Leveretts marveled at Ahmadinejad’s attention to detail as the Iranian took copious notes and strove to pronounce their unfamiliar names correctly. “He addresses every person by name. He made a serious effort to address everyone’s issue,” Flynt says. “It was really striking, the retail politics aspect.”

As former Bush White House officials, the Leveretts might seem...