A thief, Taro, has announced that he'll steal some very valuable pearls from Gregory Dillingwater during a certain week, and the police, fearing that they'll be unable to protect the pearls from the thief, who has eluded them repeatedly in the past, call in Cosmo. Despite all their preparation, the thief manages to sneak in, subdue the butler, and drug Dillingwater. However, much to Taro's surprise, the apparently drugged Dillingwater suddenly springs upon him, then removes a wig, revealing himself to be Cosmo. As Cosmo says, "the simplest method to apprehend a crook is to trap him by his own talent for making a living... a disguise for a disguise!"
This is another six page story, and again it suffers for its brevity--there's just not enough time to build up any suspense or sense of mystery. Cosmo's trick, disguising himself as Dillingwater, is a good one--good enough that (if I recall correctly) Batman used it, later--but even a good trick isn't enough to save this story.