Jeff Brant is a struggling young composer of symphonic music. Helen Borden, who lives in Jeff's apartment building, convinces him to allow their landlady's son Joe to make swing arrangements of Jeff's music, in hopes that all of them can thereby make career advances. The band sneaks into a recording studio at night to make an audition record, but when burglars rob the studio, the band members fear they will be charged with the crime. But then they learn that they have left their audition recording behind and through a fluke, it is distributed and becomes a hit by "The Mystery Swingsters." Jeff, Helen, Joe, and the rest of the band must figure how to claim rightful credit for the record without getting arrested for the robbery.