Requirements for underseas nuclear reactor power systems for small vessels include: simplified small reactor and plant control and instrumentation; long-term compatibility of fuel, structure, and coolant; and extended fuel lifetime, safety, and low cost. Neutronic qualities that reflect these requirements are: lowest critical mass for low cost and small size; low fuel concentration in the fuel elements consistent with extended fuel lifetime, small fuel effects on fuel element materials properties, and small fission-product effects; negative temperature and core geometry coefficients of reactivity, in the interest of minimizing safety and control problems, 100-g fuel burnup (100 MWd of energy). A reactor design that has these qualities uses a pressurized water moderated, beryllium (4-in.) reflected, solid fuel geometry with 0.070 g/ml 235U in the core, and zirconium fuel elements, with a fuel mass including 0.1 kg for burnup of under 0.8 kg 235U. This reactor core is 8 in. long and 8 in. in diameter, and contains 85%, by volume, of water at an operating temperature around 500°F, for a power level of 300 kW(th).