Peer punishment has been an effective means to ensure that norms are complied with in a population of self-interested agents. However, current approaches to establishing norms have only considered static punishments, which do not vary with the magnitude or frequency of norm violation. Such static punishments are difficult to apply because it is difficult to identify an appropriate fixed penalty: one that is not too weak to disincentivise norm violations and not too strong to lead to significant deleterious effects on the system as a whole (such as those incurred by losing the benefits of a member of the population). This paper addresses this concern by developing an adaptive punishment technique that tailors penalty to norm violation. An experimental evaluation of the approach demonstrates its value compared to static punishment. In particular, the results show that our dynamic punishment technique is capable of achieving norm emergence, even when starting with an amount of punishment that is too low to achieve emergence in the traditional static approach.