The max k-armed bandit problem is a recently-introduced online optimization problem with practical applications to heuristic search. Given a set of k slot machines, each yielding payoff from a fixed (but unknown) distribution, we wish to allocate trials to the machines so as to maximize the maximum payoff received over a series of n trials. Previous work on the max k-armed bandit problem has assumed that payoffs are drawn from generalized extreme value (GEV) distributions. In this paper we present a simple algorithm, based on an algorithm for the classical k-armed bandit problem, that solves the max k-armed bandit problem effectively without making strong distributional assumptions. We demonstrate the effectiveness of our approach by applying it to the task of selecting among priority dispatching rules for the resource-constrained project scheduling problem with maximal time lags (RCPSP/max).