This contribution outlines the problems and possibilities of three issues with regard to the teaching of L2 interactional competence (IC): (1) specifying IC, (2) standardising IC, and (3) translating conversation analytic (CA) insights into classroom practices. In particular, I argue for a shift of discussion from the conceptually treacherous notion of interactional competence to the CA-based model of interactional practices, call attention to the partial, and yet useful, nature of our understanding of such practices as pedagogical objects and of the developmental trajectories towards their mastery, and finally, make evident the daunting obstacles to implementing these understandings in the classroom, while offering illustrative and exemplary exhibits.