Oslin eventually made a demonstration tape of her compositions and brought them to the attention of the performance rights group SESAC. From there, it was brought to the attention of their Nashville executive, Dianne Petty. Petty encouraged Oslin's musical talent and helped bring her music to the attention of Nashville record executives. At the same time, Oslin also found work singing with Guy Clark on his 1978 self-titled album. Through Petty's assistance, Oslin acquired a "singles-only" recording contract with Elektra Records. Only two singles were issued on the label, "Younger Men" and "Clean Your Own Tables," the latter of which became a minor hit on the country chart. "My first record, `Clean Your Own Tables,` managed to get on the charts for about 15 minutes," she recalled in 1987. Elektra ultimately dropped her from their label in 1982. She returned to New York where she went into a depressive period and gained 40 pounds. She continued commercial work, but found it unsatisfying. Yet Petty continued advocating for Oslin and her original compositions were recorded by Judy Rodman, Dottie West, Gail Davies and The Judds.