Over the Southern Ocean (SO, 40°S–70°S), climate models have consistently underestimated solar reflection. Here we evaluate the relationship between cloud profiles, cloud phase and radiation over the SO in Coupled Model Intercomparison Project Phase 6 (CMIP6) models against Clouds and the Earth's Radiant Energy System and Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations. We find that the lack of solar reflection is slightly improved in CMIP6 models compared to CMIP5's, attributable to a better representation of cloud fraction and phase. We show that clouds have a different vertical structure and radiative effect south and north of where the 0°C isotherm meets the surface (∼55°S). Although the models capture the greater vertical extent of clouds south of 55°S, they fail to reproduce the observed increase in solar reflection, which we pinpoint to cloud phase biases. Increasing CMIP6 supercooled liquid cloud opacity should help reduce their persistent shortwave biases.