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Many, if not most, student trombonists have perhaps had little or no previous experience with "extended techniques"-novel or unconventional modes of sound production. To address this deficiency of experience, this document sets forth a progressive sequence of descriptive explanations and supplementary studies, which are specifically designed to assist trombonists in mastering the particular extended techniques that will prepare them to perform three of the most popular late Twentieth-Century pieces for trombone that include extended techniques-Luciano Berio's Sequenza V, Folke Rabe's Basta, and Mark Phillips' T.Rex. Following the introductory chapter, the body of the document consists of three chapters, each of which deals with one of the three solos, presenting descriptive explanations of relevant extended techniques interspersed with performance commentary (solicited from prominent trombonists) and supplementary studies (composed by the author). The studies presented in each chapter are specifically geared toward mastering the extended techniques as they relate to the music of each particular solo. They are also especially focused toward learning the more difficult passages of music in each solo.