The Scottish Government’s policy of minimum unit price (MUP) for alcohol has received significant scholarly attention. Much of the focus of this literature has been on the efforts by sections of the alcohol industry to oppose the policy, including attempts to ‘frame’ key terms of the debate and an understanding of its legitimacy and effects within the wider field of interpretative policy analysis. The present article builds on these studies by re-conceptualizing the MUP debate through the lens of post-structuralist discourse theory and the logics of critical explanation that emerge from this. It argues that the success and failure of MUP (as a projected social logic) can be understood through the shifting coalitions of actors that emerged (political logics) and the affective hold that industry narratives were able to exert (fantasmatic logics) in this context. While focused on UK alcohol policy, the article speaks to a wider research agenda on the ‘commercial determinants of health’ and, through the application of the critical logics approach, offers new analytical insights beyond those provided by existing models of industry influence. Similarly, it contributes to the field of post-structural policy analysis through its novel focus on the role of commercial entities as health policy actors.