Using a maximum entropy technique, we estimate the market shares of each firm in an industry using the available government summary statistics such as the four-firm concentration ratio (C4) and the Herfindahl-Hirschmann Index (HHI). We show that our technique is very effective in estimating the distribution of market shares in 20 industries. Our results provide support for the recent practice of using HHI rather than C4 as the key explanatory variable in many market power studies, if only one measure is to be used.