Summary: We show that, in repeated common interest games without discounting, strong `perturbation implies efficiency' results require that the perturbations must include strategies that are `draconian' in the sense that they are prepared to punish to the maximum extent possible. Moreover, there is a draconian strategy whose presence in the perturbations guarantees that any equilibrium is efficient. We also argue that the results of \textit{L. Anderlini} and \textit{H. Sabourian} [Econometrica 63, No. 6, 1337--1369 (1995; Zbl 0841.90129)] using perturbation strategies that are cooperative (and hence nondraconian) are not due to computability per se but to the further restrictions they impose on allowable beliefs.