This paper draws on the narratives of parents of disabled babies in order to conceptualise notions of enabling care. This analysis emerges from the Sheffield site of an ESRC research project Parents, Professionals and Disabled Babies: Identifying Enabling Care, which brings together the Universities of Sheffield and Newcastle-upon-Tyne. The linear heroic narrative is a dominant theme within Western culture. It is competitive and individualistic and tends to be future-orientated in that actions conducted in the present are evaluated according to later outcomes. This linear narrative places much store on modernist interventions such as medicine, and tends to uphold professional boundaries and hierarchies. In the lifeworlds of parents, usually mothers, of disabled babies, this narrative can reinforce disempowering interpretations of disability and impairment. On the basis of 25 in-depth interviews, accompanying stories and ethnographic data, this paper suggests that parents are developing counter-narratives which, at times, resist linear life models and free parents to enjoy their children as they are. If life is perceived as an open book rather than as a concluding chapter, parents are able to develop stories that are neither linear nor heroic but present and becoming.