Two different primary coolants, Li and 83Pb-17Li, have been examined for use in Pulse*Star, a pool-type inertial confinement fusion reactor, and a balance-of-plant design has been generated for each coolant. The use of 83Pb-17Li eliminates concern about the large amount of stored chemical energy found in pure Li fusion reactors. A secondary loop was not included in the 83Pb-17Li coolant design because of the relative nonreactivity of lead-lithium. The design utilizing Li as a primary coolant includes a sodium secondary loop to prevent direct contact between irradiated Li and high-pressure water in the case of a steam generator leak. The secondary loop requires additional piping, pumps, heat exchanger area, and steam generator buildings. These additional costs are mitigated by the low pumping power requirement of Li compared with that of high-density 83Pb-17Li. A cost analysis revealed that the additional costs of the Li coolant design are only slightly greater ($13.5 million) than the cost savings due to the lower pumping power. Preliminary studies indicate that tritium containment will be more costly for the 83Pb-17Li coolant design than for the one involving pure Li because the insolubility of tritium in 83Pb-17Li creates large driving forces for tritium leakage into the surrounding plant. The tradeoff between the two safety concerns of chemical stability in the case of 83Pb-17Li and practicable tritium containment in the case of pure Li needs to be investigated.