This essay will use the documentation surrounding the objects displayed in Cuba's Museum of Legal Medicine (among them, an “aero buey fantastico” made out of bread crumbs by inmates at Havana's Hospital for the Demented) to examine the logics that bound ethnography, medicine, policing, and collecting to one another in the early decades of the twentieth century. In a 1930 pamphlet describing this collection, the authors suggest that the museum will serve national aspirations to high-quality scientific research. But this pamphlet, like some subsequent interpretations, obscures a messier early history that diminishes the importance of the nation as an organizing principle and is rooted instead in a transnational traffic in “museum” pieces, local networks of intellectual production, and changing therapeutic practices within hospitals and prisons. The article argues that the stated logics of this collection don't quite contain all the objects, some of which exceeded and overflowed the categories in question. Both powerful and incomplete, the museum's “system” holds many of the objects together but also fails to wholly incorporate all of them. The essay will also consider the relationship of policing to this grammar of collecting, and suggest that putting a history of policing together with a history of museums indicates that the collecting guided the policing as well as the other way around.