Jazz has been a familiar element of secondary music curricula in the United States since the late 1960s (Worthy 2013). Yet, as broader social dialogue addresses equity and justice concerning gender and sexuality, secondary instrumental jazz education remains underrepresented in those discussions. Pressures to conform to heteronormative notions and performances of gender and sexuality in this field demand participants deemphasize aspects of their identities in order to avoid stigmatisation, a practice known as 'covering' (Yoshino 2002). Pressure to perform gender and sexuality 'intelligibly' (Butler 1999) can serve as motivation toward assimilation or as a force of discrimination (Yoshino 2002). Thus, in this paper I argue historically that established and contemporary instrumental jazz pedagogies comprise acts of discrimination. I recommend ways of troubling heteronormativity embedded in conventional methods of teaching aspects of instrumental jazz such as improvisation and swing feel. Suggestions are offered for shifts toward diminishing discriminatory pressures to cover.