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In the audience of a radio broadcast, singer Helen Borden's dress catches on a button of classical composer Jeff Brant's suit, causing a major disturbance and resulting in their ejection from the studio. Later, Helen and Jeff discover that they live in the same boardinghouse run by Mrs. Olsen, whose son Joe is attempting to start a swing band. Unknown to Jeff, Joe has been arranging Jeff's classical compositions for the band. Joe invites Helen to join the band and she, in turn, convinces Jeff to join them. The band is so poor, however, that the musicians must practice on the instruments in Scottish pawnbroker Alex MacDevin's store. Alex agrees to loan the band the instruments long enough to record a demonstration record. A band member's father is night watchman at the Four Star Record Co., and his son "borrows" his duplicate key so that they can make a record. As they finish, however, two crooks break into the studio, blow open a safe and steal bonds, forcing the band to flee without the valuable recording. MacDevin suggests that the band find a radio sponsor, but ends up agreeing to sponsor the broadcasts himself. Jeff and Joe arrange with radio station executive Digby for a slot at 5:00 a.m. Meanwhile, Stuyvesant, Four Star's president, finds out that, due to a mistake, 6,000 copies of the record have been made. As he believes that the robbers may have made the recording, he orders it to be distributed, calling the group "The Mystery Swingsters with Mademoiselle X." The band's live broadcasts generate a lot of interest but they have misunderstood the terms of the contract and MacDevin owes the station much more money than anticipated. Meanwhile, the record becomes a number one best-seller. Another band claiming to be "The Swingsters" is signed to a long-term radio contract, but they are suspected of being the safecrackers and are arrested, just before their initial broadcast, by bungling police detectives Crandall and Murphy. Jeff, Helen, Joe and the band substitute for the arrested musicians, but are heard by Stuyvesant and are arrested as well. While the band is being questioned at the police station, the two burglars are brought in, having been arrested for parking next to a fire hydrant and discovered to be in possession of the stolen Four Star bonds. Jeff, Helen, Joe and the band then sign contracts with both the record company and the radio station, with Alex acting as their very astute manager.