The notion of the `core set' usually refers to that group of scientists involved in the eventual resolution of a given technical controversy. Drawing upon actor-network theory, we suggest that such core sets, especially at science/public interfaces, are, in fact, constituted from generalized agonistic sets which entail `non-technical' issues - political, ethical, economic. Interview material with scientists who use animals in their research showed how they attempted to demarcate such a core set with their public critics. We consider how they constricted the core set by discursively demarcating the criteria for membership. These included `rationality' and `emotional authenticity'. Elaborating on Collins' use of `core set', we suggest that these discourses indicate that scientists are potentially engaged in actively constituting a core set by setting out cultural criteria for membership. Contrary to the focus of actor-network theory upon `definitive' enrolment, we found that scientists can also engage in characterizing suitable antagonists. As a supplement to both core set and enrolment, we suggest the concept of `envelopment'.