Cross-flow turbine (known as vertical-axis wind turbines or “VAWTs” in wind) blades encounter a relatively undisturbed inflow for the first half of each rotational cycle (“upstream sweep”) and then pass through their own wake for the latter half (“downstream sweep”). While most research on cross-flow turbine optimization focuses on the power-generating upstream sweep, we use single-bladed turbine experiments to show that the downstream sweep strongly affects time-averaged performance. We find that power generation from the upstream sweep continues to increase beyond the optimal tip-speed ratio. In contrast, the downstream sweep consumes power beyond the optimal tip-speed ratio due to unfavorable lift and drag directions relative to rotation and a potentially detrimental pitching moment arising from rotation-induced virtual camber. Downstream power degradation increases faster than upstream power generation, such that downstream sweep performance determines the optimal tip-speed ratio. In addition to performance measurements, particle image velocimetry data are obtained inside the turbine swept area at three tip-speed ratios. This illuminates the mechanisms underpinning the observed performance degradation in the downstream sweep and motivates an analytical model for a limiting case with high induction. Performance results are shown to be consistent across 55 unique combinations of chord-to-radius ratio, preset pitch angle, and Reynolds number, underscoring the general significance of the downstream sweep.