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Broadway dancer Tallulah Winters is about to sail to Puerto Rico with Tommy Dorsey and his Orchestra when she is summoned to the office of Inspector Davis. Davis asks her to perform an important service for the government by taking the most powerful magnetic mine in existence on her voyage, explaining that it cannot fall into enemy hands and she would never be suspected of hiding it. He then gives her half of an old coin and says that she will be contacted onshore by the person with the other half. Unknown to Tallulah, Davis is part of a spy ring headed by Dr. Farno, who devised his plan after reading a dime magazine story written by Merton K. Kibble. Merton, who is a chronic hypochrondriac, is so prolific that he employs three secretaries, but suffers from stress over all of his deadlines. Because his assistant, "Skip" Owens, wants to romance Talullah's assistant, Fran Evans, Skip convinces Merton to take the cruise to Puerto Rico when Merton's doctor refuses to treat his imagined ailments. Onboard ship, Merton and Tallulah meet and are soon attracted to each other. Meanwhile, real government agents H. U. Bennett and his assistant, Art Higgins, receive permission from the ship's captain to search for the missing mine, which they know must be onboard. The night before the ship docks, while attending a costume party, Tallulah demonstrates for Merton that she once used Morse Code for a tap dance in a show. He asks her to tap out "You're wonderful," then tells her he loves her. Later, in his cabin, Merton receives a telegram from his publisher, spurring him on to work on a new story. As he and Skip are discussing the plot of the story, Tallulah walks by his window and, misinterpreting what he is saying, concludes that Merton is really a cad. The next day, Farno and his cohort, Pietro Polesi, wait for Tallulah on the dock, while Merton goes to her cabin. He is shocked and confused by her strange reaction to him, and when he tries unsuccessfully to talk with her on deck, he accidentally switches suitcases with her. Tallulah then leaves, not knowing that Merton now has the bag with the mine in it. Onshore, as Bennett and Higgins discuss the case with a local government agent, Bennett recognizes a photograph taken of Farno at the dock. Bennett then concludes that it is Farno who has paid for the entertainers to come to Puerto Rico. Meanwhile, in Tallulah's dressing room on Polesi's nightclub ship, Polesi hands her the matching half coin and tells her that her contact is Dr. Farno, who wants her to give him the mine between shows that night. After Polesi leaves, Talluluh goes to get the suitcase with the mine and realizes that she has Merton's case instead of her own. She then sneaks into Merton's room and, following a series of mix-ups with Merton and the house detective, finally gets away with the right case. She gives the mine to Farno, who is concerned when she casually tells him about the mix-up. He then tells Tallulah that Merton, who is just boarding the ship at that moment, is actually a spy. She does not believe Farno and after Skip and Merton are brought to Farno's office, they are imprisoned by one of Farno's thugs. Using a ploy he concocted for a book, Merton soon breaks free, taking Skip with him. As Tallulah prepares for her show, Bennett comes to her with his government badge and she thinks that he is working with Farno, but when Farno's thugs take Bennett prisoner, she begins to realize the truth. Farno plans to dispose of Tallulah, but because the crowd is calling for her, realizes that she must perform, and allows her to go onstage, warning her not to try anything. While she dances, Tallulah uses her Morse Code tap trick to signal an SOS. Higgins, who is in the audience, "reads" the signal, then motions to her to continue. When her message is complete, he signals that he understands, and Merton and Skip, who also realize what Tallulah is doing, help him. They go to Farno's office and after a scuffle, Skip and Merton escape with the mine and enter a lifeboat. With Tallulah's help, they are lowered into the ocean and after rowing for some time, eventually land on an American submarine.