Although a variety of goodness-of-fit test statistics are used by applied researchers, studies of their power have been limited. This paper investigates the simulated power of six goodness-of-fit test statistics for discrete data for small sample sizes. The null distribution is uniform and the simulated power of each of the test statistics is calculated for a number of alternative distributions including trend, triangular, flat/platykurtic type, sharp/leptokurtic type and bimodal. KEY WORDS: Goodness-of-fit, simulation.