The agency is hired by Joe Fairgate to locate his sister, Sally Fairgate, who disappeared in a "she was there, then all of a sudden she wasn't" scenario. Although the Fairgates are extremely wealthy, the Angels and Joe believe, since there is no ransom request, that Sally's disappearance has nothing to do with their wealth, but rather something to do with the location where she went missing, a three day/thirty hour ballroom dance competition at the struggling Dancetown dance hall where Joe and Sally were entered and, coming out of nowhere, became the favorites to win the $5,000 first prize. Attending Dancetown as potential contestants, the Angels and Bosley end up investigating many of those involved directly with the competition: Dancetown's co-owners, P.J. Wilkes and Al Norman, who, on the surface, have a film noir shadiness to them, especially in Norman idolizing the classic movie tough guys; Elton Mills, the bandleader who longs to return to the big band era; and Billy and Betty, the band's young vocal couple whose usual taste in music isn't found in such dance halls. But who becomes their chief suspect is "couple number 6", who were favored to win the competition before Joe and Sally arrived on the scene, with the male of the couple having an especially easily triggered temper in achieving the prize, the question being at any cost?
—Huggo