In societies where the use of computers is pervasive, individuals who resist using the technology are often studied in order to determine how susceptible their views might be to change. This research takes a different approach, focusing not on the non-use of computers as a problem but as an opportunity to explore how the proponents of such views make sense of computers and computer use and to accord respect for, rather than dismissal of, their views. Underpinned by a narrative sense-making approach, the investigation examines older non-users' discursive performances of rejection and the ways in which they draw on and position themselves in relation to dominant and emerging socio-cultural narratives of technology and the ways in which those performances are circumscribed by particular value systems or choice behaviours. Participants drew on three prominent socio-cultural narratives in making sense of computers and in performing rejection: computers benefit older people; society discriminates against non-users; and don't need computers, don't want computers. These three narratives work together to enable non-users to justify their rejection of computer use. The study makes a contribution to the literature by highlighting dimensions of older people's relationships with computers not previously identified, including an appreciation for the complex and often tension-filled process by which determinations of rejection are made.