In 1936, Leslie caught the attention of a talent scout from Metro-Goldwyn-Mayer (MGM) when the three Brodel sisters were performing in New York. She was given a six-month contract with the studio, earning $200 per week. While working at the studio, she attended MGM's Little Red Schoolhouse with other child actors like Mickey Rooney and Freddie Bartholomew.  Her first film role was in Camille (1936), a romantic drama starring Greta Garbo and Robert Taylor. She played Taylor's younger sister Marie Jeanette, but her speaking scenes were deleted and she was uncredited. MGM had trouble finding suitable roles for her, and she was let go by the studio along with Deanna Durbin. Leslie returned to New York, working on the radio and as a model. During this time, her older sister Mary was signed to Universal Studios. Leslie returned to Hollywood with the rest of her family, working for different studios as a freelancer. She mainly worked for RKO Pictures.  Leslie was selected to play a small role in Men with Wings (1938). While shooting the film, director William A. Wellman discovered that Leslie's mother had lied about her daughter's age and that she was only thirteen years old. For the remainder of the filming schedule, Wellman replaced her with Mary.  Leslie gained her first credited role in Winter Carnival (1939) as Betsy Phillips. She was chosen for the part because the director was searching for an actress with a southern accent. She was billed as Joan Brodel. Later that year, she co-starred with Jimmy Lydon in Two Thoroughbreds, in which she played the daughter of a horse owner.  At age 15, Leslie was selected by a group of Hollywood directors as one of 13 "baby stars of 1940."

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