An algorithm is presented to compute an optimal (s, S) policy under standard assumptions (stationary data, well-behaved one-period costs, discrete demand, full backlogging, and the average-cost criterion). The method is iterative, starting with an arbitrary, given (s, S) policy and converging to an optimal policy in a finite number of iterations. Any of the available approximations can thus be used as an initial solution. Each iteration requires only modest computations. Also, a lower bound on the the true optimal cost can be computed and used in a termination test. Empirical testing suggests very fast convergence.