To estimate the age distribution of a fish population, a two-phase stratified sample design is proposed. Bayesian methods are employed to determine (a) optimal estimators of the desired population proportions; and (b) the optimal choice of second-phase sample sizes subject to a fixed budget. A summary of the results of some numerical examples is presented. These examples demonstrate typical expected gains obtained by using the Bayesian optima as compared to alternative choices of second-phase sample sizes suggested in the substantive literature.