This paper builds on prior work of the authors by developing a shortcut method for determining approximately optimal (s,S) inventory policies for use in a periodic review inventory system in which shortage costs are assessed. The method seems to work well under the conditions for which it is designed, which include requiring that the shortage cost be relatively high and that the variance in demand be relatively low. The method is then adapted to the case where a service level constraint on expected shortages per period is imposed. The method again appears to work well and, in particular, seems to yield better control than do some continuous review approaches, in that the actual service levels are closer to the intended ones.