Lakes Mead and Powell in the Colorado River Basin are a critically important source of water and hydroelectric power for the western United States. While the policies currently regulating the basin are set to expire by 2026, planning remains challenging due to intertwined climate variability and policy uncertainties. Based on streamflow projections from 10 dynamically downscaled CMIP6 global climate models, we evaluate future conditions at both reservoirs under existing and alternative policies, including the most recent proposals at the time of this study. We build upon our CMIP6 ensemble by developing methods that add and remove internal variability to robustly characterize how the policies respond to future hydrologic conditions. Under existing policy, the reservoirs will face substantial risks before 2060, with at least 80% likelihood of reaching dead pool at least once. Adopting any of the alternative policies can reduce but not eliminate the risks of Mead reaching a dead or inactive pool, while the risks at Powell remain high. All policies can exhibit tipping points where the reservoir levels can change rapidly with only a slight change in natural flow. We argue that a robust policy should buffer the reservoir from such sudden changes under all conditions, and yield reservoir storage and water delivery outcomes consistent with changes in hydrologic conditions.