Through exchanges within a doctoral supervision, the authors explore a range of dilemmas and challenges for reflexive inquiry. These include the problematic business of naming, the impossibility of objective separation of self from research, the merging of researcher subjectivities, and differences between performance and performativity. We note the educational potential in what can conventionally be considered “unprofessional” approaches to qualitative inquiry: neologisms, personal experience, stories, conversations, music, poetry, paintings, and film. We engage in reflexive interactions with each other and with such “data.” This was undertaken in the spirit of jazz improvisation—an unrehearsed performance—something that “happened,” an unplanned educational event but also an agency enabled by structure.