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Barack Obama entered the Oval Office implicitly promising to single-handedly reinvent America's image in the world. And if his administration had a strategy for reducing the long-term threat of violent extremism, it boiled down to this: Put the president in front of a microphone, and let his natural charisma do the work.

This approach has paid some dividends; multiple surveys show that views of the United States have noticeably improved over the last year. But winning the war of ideas means making progress on a much wider, and arguably more important, set of indicators. It means putting together carefully calibrated actions and initiatives that together make up public diplomacy, which is often wrongly conflated with old-fashioned public relations. It's not the same...