This paper introduces three new methods for computing approximately optimal inventory policies for discrete time shortage cost systems. Two of the methods are shortcuts based on the method of Freeland and Porteus  and one is a heuristic that takes a standard continuous review approximation and makes three modifications: (10 a new boy adjustment due to Wagner et. al. , (2) a discrete period adjustment inspired by to the normal approximation. These methods and a number of other competing methods are evaluated on a test bed of 1200 cases. One of the shortcuts and the new heuristic method performed very well, with a percentage error of their average costs being around one percent. Some commonly referenced competing methods had percentage errors of over 10% and a commonly cited continuous review approximation had a percentage error of over 80%. The numerical results are broken out to yield further insights into the relative strengths of the various methods.