Frequency analysis is commonly used in hydrology to define flood plains, design hydraulic structures, and aid in watershed planning and management. Although design event magnitudes may be determined analytically by using probability distributions, the analytical determination of confidence limits for the design event is not easy. Using the alternate method of moments to determine confidence limits involves an assumption of normality of the distribution of design events. It is shown by data generation that this assumption is valid for quite small samples. Tables are given to compute confidence limits in this manner for several common probability distributions.