A large-scale two-dimensional computational fluid dynamics study is conducted in order to maximise the power output and smoothness of power delivery of a free-stream water wheel, a low-impact hydropower device. Based on models and methods developed in previous research, the study uses a genetic algorithm to optimise the geometry of a wheel with a given radius and depth, maximising two objective functions simultaneously. After convergence and suitable post-processing, a single optimal design is identified, featuring eight shortened blades that become fully immersed at the nadir point. The design results in a 71% reduction in blade material and a 113% increase in the work ratio while improving the hydraulic power by 8% compared to the previous best design. These characteristics are applied retroactively to a broad family of designs, resulting in significant improvements in performance. Analysis of the resulting designs indicates that when either the hydraulic power coefficient, rotor power coefficient, or work ratio is considered, free-stream water wheels with fully immersed blades, whose power mechanisms are shown to rely on lift, as well as drag, outperform all other designs studied so far.