The optimization problem consists of four key elements: a figure of merit for the reactor, a technique for estimating the neutronic performance of the blanket as a function of the design variables, constraints on the design variables and neutronic performance, and a method for optimizing the figure of merit subject to the constraints. The first reactor concept investigated uses a liquid lithium blanket for breeding tritium and a steel blanket to increase the fusion energy multiplication factor. The capital cost per unit of net electric power produced is minimized subject to constraints on the tritium breeding ratio and radiation damage rate. The optimal design has a 91-cm-thick lithium blanket denatured to 0.1% /sup 6/Li. The second reactor concept investigated uses a BeO neutron multiplier and a LiAlO/sub 2/ breeding blanket. The total blanket thickness is minimized subject to constraints on the tritium breeding ratio, the total neutron leakage, and the heat generation rate in aluminum support tendons. The optimal design consists of a 4.2-cm-thick BeO multiplier and 42-cm-thick LiAlO/sub 2/ breeding blanket enriched to 34% /sup 6/Li.