Performance of an approximation to continuous review (s,S) inventory policies under constant lead time, full backlogging, compound renewal demand, and a linear cost structure is examined. The approximations are based on a lower bound for the optimal order-up-to level and the corresponding best reorder point. It is shown that the approximate policy is unique and that it performs better under relatively higher shortage costs, longer lead times, and lower set-up costs. Both exact and approximate policies are computed and the corresponding objective function values are compared under a large number of different parameter settings. The average relative approximation error is found to be 2·23% with a 27-fold average reduction in computing times.