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Many mathematics education scholars agree that university mathematics needs to do a better job of supporting equitable classroom practices. Scholars in K-12 education have offered myriad frameworks for equitable pedagogy, yet there is limited work exploring the applicability of these practices to the undergraduate mathematics setting. Since K-12 teachers operate in a different institutional context, it is unclear the extent to which the same strategies work in university classrooms. In this study, I interviewed seven math doctoral student instructors to understand their perceived barriers to implementing equitable practices, in the form of culturally sustaining pedagogical practices, in undergraduate math classrooms. Instructors indicated instances in which institutional obligations, obligations to be honest with students, and obligations to respect student agency and feedback restricted their ability to implement various CSP recommendations.