A methodology is developed to determine the fuel pin enrichment distribution that yields the best approximation to a prescribed power distribution in boiling water reactor fuel bundles. Optimal pin enrichments are defined as those that minimize the sum of squared deviations between the actual and prescribed fuel pin powers. A constant average enrichment constraint is imposed to ensure that a suitable value of reactivity is present in the bundle. In the special case when each pin in the bundle is permitted to have a different enrichment value, the solution is obtained iteratively using a projected gradient algorithm. Gradient information and power distributions are computed by adapting the response matrix method to fuel bundle power calculations. In the general case when the fuel pins are limited to a few enrichment types, one obtains a combinatorial optimization problem. Formally, the assignment of an enrichment type to the various fuel pins is made through a matrix of Boolean variables. Since the optimal assignment, as well as the optimal values, of the enrichment types must be determined, a nonlinear mixed integer programming problem must be solved. Algorithms based on either exhaustive enumeration or branch and bound are shown to give a rigorous solution, but are computationally overwhelming. Solutions that require only moderate computational effort are obtained by assuming that the fuel pin enrichments in the combinatorial problem maintain the ordering that was found in the special case mentioned above. Search schemes using branch and bound now become computationally attractive. An adaptation of the Hooke-Jeeves pattern search technique is shown to be especially efficient.