Are ordinary proper names rigid when they occur in fictional discourse? In previous work (García-Carpintero 2010a) I have argued that they are not, at least when we consider the core case of textual fictional discourse, and also the case, dependent on it, of paratextual fictional discourse. From a perspective on such discourse which—on my reading of Koťátko (2004) and (2013)—I understand to be not far away from mine, Petr Koťátko (2010) argues that they are not: “proper names remain rigid designators in Kripke’s sense ... even if transferred from ‘everyday’ communication to literary texts” (op. cit., 94). After explaining how I understand the relevant concepts in the first section, I’ll critically take up Petr’s arguments in the second.