The most celebrated FBI agent is recruited to catch a telepath in the Yucca Flats Research Lab who is selling national secrets. The agent has been very successful in past cases, but he really feels rather low, because he thinks he is just lucky and not good. He caries this attitude throughout the story, acting like a depressed puppy.
So how do you catch a telepath? With another telepath, of course. There is a stop along the way to check out a catch-22 telepath detector machine which will only detect if someones mind is being read, maybe. The nationwide search for telepaths turns up several, but unfortunately, they are all in mental institutions and loonier than Bugs Bunny. The FBI boss orders the agents to humor the crazy telepaths (one not so crazy after all) so they will help catch the criminal.