The increasing need for miniaturization of radial pumps has been expressed across a variety of fields including rocket propulsion, which has driven research into their optimization. The literature provides design recommendations aimed at mitigating the adverse effects associated with the low Reynolds regimes of these small-scale pumps. This study applies some of these adjustments to a small, high-speed turbopump equipped on the Navier rocket engine. A sensitivity analysis is performed on the outlet total pressure and efficiency of the pump in order to gauge the effectiveness of the design changes. It is found that the impeller outlet width has the most on influence on the pressure, while the efficiency is most sensitive to the pump’s inlet diameter. A regression on the sample points generated for this analysis is then performed, becoming the basis for a surrogate model used in a simple optimization routine of the pump impeller. An optimized version of the Navier pump is obtained, with an outlet pressure fulfilling the engine’s requirements, and an increased overall efficiency.