During his essay "Composition with Twelve Tones" (1941), Schoenberg points to the compositional skill required to manage the relationship between the Trio's canonic voices:"The Trio of this Menuet is a canon in which the difference between the long and short notes helps to avoid octaves. The possibility of such canons and imitations, and even fugues and fugatos, has been overestimated by analysts of this style. Of course, for a beginner it might be as difficult to avoid octave doubling here as it is difficult for poor composers to avoid parallel octaves in the 'tonal' style. But while a tonal composer still has to lead his parts into consonances or catalogued dissonances, a composer with twelve independent tones apparently possesses the kind of freedom which many would characterize by saying 'everything is allowed.' 'Everything' has always been allowed to two kinds of artists: to masters on the one hand, and to ignoramuses on the other." There is more disdain than detail in Schoenberg's commentary; about compositional practice, he writes only of "avoiding octaves." As shown later in this paper and as one might suspect from a composer of Schoenberg 's experience and ability, other more sophisticated methods of contrapuntal organization saturate the "Trio." Although undergraduate theory curricula often leave only a short time for twelve-tone study, it is imperative that we teach students to appreciate such row combination relationships. For if students learn nothing of Schoenberg's "mastery" from our teaching, they are unlikely to respect the twelve-tone repertoire. After all, anyone could write a canon if the harmony didn't matter! With the pedagogical goal of equipping undergraduate students to uncover or at least understand and appreciate such relations, the paper presents an analytic framework with accompanying vignettes, analyzes the "Trio," and offers musically convincing ways to present these analytic findings in a classroom setting.