In this paper I ask what an investigation of the Budapest model of supervision may add to our psychoanalytic imagination. The Budapest model confronts us with a number of crucial questions for contemporary psychoanalysis, including the question of envisioning ways of working on the countertransference of the analyst. I discuss the lack of memory that surrounds the Budapest model, and I read it in relation to the unsettling issues it stirs up, including those of authority, horizontality, and the ethics of psychoanalysis. In the Budapest model, supervision can be seen as a form of “double dreaming” or of “dreaming up of a dream”. In particular, in drawing on the writings of Sándor Ferenczi and Michael Balint, I point to some principles behind the Budapest model and to the epistemic, technical, and ethical implications of their ideas. I also work toward a Ferenczian “translation” of the idea of “parallel process”.