A new method, recently proposed by Porteus, for obtaining approximately optimal (s,S) inventory policies was evaluated numerically. When demand was normally distributed, the method performed very well. The performance was good but diminished somewhat when demand followed a negative binomial distribution which was approximated by a normal distribution for purposes of the method. The empirical method of Wagner, O’Hagan, and Lundh was evaluated concurrently. It also performed very well. Although its performance was not as good as that of the new method, it required less computational effort. The question of the extent to which application of one of these approximate methods can provide improved performance in practical periodic review systems was raised. A partial answer was obtained by examining the performance of policies found by using a continuous review model. Both the new method and the empirical method outperformed these policies. Such a finding is consistent with the tests conducted by Wagner, O’Hagan and Lundh.