Intraspecific cooperation and interspecific mutualism often feature an asymmetry in the scope for exploitation. We investigate the evolution of indirect reciprocity in an asymmetric game, loosely modelled on interactions between cleaner fishes and clients, in which 'actors' can choose to help or to exploit a 'recipient' that approaches them, while recipients can only choose whether or not to approach an actor (based on the observation of its behaviour towards others). We show that when actors vary in state over time, in a manner that influences the potential gains from exploitation, an equilibrium is possible at which recipients avoid actors whom they have observed exploiting others in the past, and actors help when the potential gains from exploitation are low but choose to exploit when the potential gains are high. In this context, helping is favoured not because it elicits reciprocal altruism ('help so that you may be helped'), but because it facilitates profitable exploitation ('help so that you may gain the opportunity to harm'). The cost of helping one recipient is thereby recouped through exploitation of another. Indirect reciprocity is thus possible even in asymmetric interactions in which one party cannot directly 'punish' exploitation or 'reward' helping by the other.