This paper studies the numerical computation of the two parameters (the reorder level s and the order up to level S) of inventory policies for discrete time shortage cost systems. Our goal is to obtain approximately optimal policies with little computational effort. The paper introduces three new methods that are designed to achieve this goal. Two of the methods are shortcuts based on the method of J. Freeland and the author [ibid. 28, 353-364 (1980; Zbl 0425.90023)] and one is a heuristic that makes several modifications to a standard continuous review approximation. The paper provides a fairly detailed survey of other methods for easily computing approximately optimal inventory policies. It then numerically compares all these methods on a reasonably broad range of problems. One of the shortcuts and the new heuristic method performed very well: the percentage error of their average costs was approximately 1%. Some commonly cited competing methods had percentage errors of over 10% and a commonly cited continuous review approximation had a percentage error of over 80%. To study the effect of extreme parameter choices in the test bed, the paper introduces a procedure to determine a subset of the parameter values, called the 1% contiguous test bed, for which each method performed well. The results show that, depending on the range of values that apply in a given practical situation, either (i) any of a large number of methods will yield good performance or (ii) a carefully selected method can achieve superior performance.