 On November 29, 1965, Closter was selected by the Cleveland Indians in the Rule 5 Draft.A few months later, on April 6, 1966, before ever playing a game in the Indians organization, Closter was purchased by the Washington Senators.Closter played only one game in the Senators organization, pitching 0.1 innings against the Baltimore Orioles in his MLB debut, before being purchased again by the Yankees on May 3, 1966.