"Them There Eyes" is a jazz song written by Maceo Pinkard, Doris Tauber, and William Tracey. It was published in 1930. One of the early recorded versions was done by Louis Armstrong in 1931. It was made famous by Billie Holiday who recorded her version in 1939 on Vocalion Records.
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http://en.wikipedia.org/wiki/Them_There_Eyes