A method for estimating the size of a heavily exploited animal population from catch data and relative-harvest-effort data is presented. The method assumes a competing-risk model of adult deaths and captures that is similar to the hazard-regression model of Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187-220). This model avoids making any assumptions about birth rates or juvenile mortality rates, and allows the user to incorporate an arbitrary number of time-dependent covariates into the natural and catch hazard functions. Estimates of the population's size, together with asymptotic error bounds and predictions of subsequent catches, are derived from maximum likelihood estimates of the parameters of the model. A simulation study is presented which indicates that this method is far more accurate than previously available catch-effort techniques. The method is illustrated with some fisheries data. A series of models is fitted to the data with the objective of improving the goodness of fit while maintaining biologic plausibility of the model. In this example a 68% reduction in the mean sum of squares for error is obtained and the accuracy of future catch predictions is greatly improved. This method is particularly appropriate for estimating the sizes of commercially exploited aquatic populations whose sizes are too large to make mark-recapture techniques feasible, and which are not amenable to line-transect techniques.