We live in the Fake News Era. When a news outlet publishes an unfavorable story about someone, he or she screams, “Fake news.” Bots, internet trolls, and disreputable web sites promote phony stories, undermining the credibility of honest reporters and publications.

It’s a tricky time to work in media relations. Reporters are suspicious. Audiences are dubious and distracted. Executives at companies we advise are impatient and want accurate—and favorable—coverage.

So how do we deliver...