1.Josh Parsons (2004) offers an ingenious plan for drinking alcohol while avoiding any hangover, based on combining a ‘hair of the dog’ cure with a supertask. Critical attention has focused almost exclusively on the supertask. Is it coherently defined? (Williams 2004.) Are there infinitesimal hangover periods left unaccounted for? (Parsons 2006.) Can analogous supertasks be used for other useful ends? (Prosser 2006.) In so doing, critics have missed a more basic flaw in Parsons's proposal. My purpose in this short note is to argue that concern over the supertask is beside the point. I shall highlight an incoherence in the apparently innocuous assumptions about drunkenness and hangovers which Parsons makes at the outset. These turn out to be paradoxical in their own right. And without these assumptions the supertask remedy does not even get off the ground.