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CDUniverse has an audio clip of "Baby, Don't You Cry (The New Swingova Rhythm)" by Ray Charles on the album listed below. Click on the album name and you will be taken to a list of albums, including the one below, that include the above song. (Note: Those albums with music note icons all have song clips. To see the entire list of CDs, you may need to scroll down all the way to the bottom as many songs have lyrics and other information displayed at the top.)
Ray Charles - Ray Charles