Research that has explored the lives of men and women recovering from heroin addiction has reported that users often claim that they ‘just want to be normal’. Working within a Foucauldian tradition, we argue in this article that the notions of ‘governmentality’ and the ‘norm’ are especially apposite to understanding the ubiquity of this aspiration. Here we focus not on the formal institutions of governance that encourage individuals to adhere to social, cultural and political norms, but rather seek to explore recovering users’ accounts of normality as they are envisaged and expressed. The reported empirical data were generated from interviews with 40 men and women in England at various stages of recovery from heroin use. The analytic focus is upon the accounts of normality articulated during the interviews in order to identify the ways in which being normal is presented by the participants. In keeping with the methodological tradition of discourse analysis we identify six discursive repertoires of ‘normality talk’ that transcend the accounts. It is concluded that the negotiation of normality is a precarious route for this social group. Articulations of a desire to be normal are replete with tensions; there are expressions of both resistance and resignation. Despite claims by some contemporary social theorists that diversity is the ‘new normality’, the accepted bounds of ‘difference’ are limited for those who have been addicted to heroin.