Shifts in Southern Ocean (SO, 40-85S) shortwave (SW) cloud feedback (SWFB) towards more positive values are the dominant contributor to higher effective climate sensitivity (ECS) in Coupled Model Intercomparison Project phase 6 (CMIP6) models. The positive shift in SWFB in CMIP6 global climate model (GCMs) can be traced back to the greater reduction in low cloud cover and the weaker cloud liquid water response to warming in the SO. To evaluate how realistic the CMIP6 cloud response is, we connect the SO SWFB to changes in column-integrated liquid water mass (LWP) and the susceptibility of albedo to LWP in 50 CMIP5 and CMIP6 GCMs. In turn, we predict the responses of SO LWP to warming using a cloud-controlling factor (CCF) model. The combination of the CCF model and radiative susceptibility explains about 50% of the variance in the GCM-simulated SWFB in the SO. Observations of SW radiation fluxes, LWP, and reanalysis of CCFs are used to constrain the SO SWFB. This yields a constrained response of SO LWP to warming of 2.89-4.41 gm-2K-1, relative to the total GCM range of -0.48-9.33 gm-2K-1. The susceptibility of albedo to LWP is constrained to be 0.41-0.86 (kgm-2)-1, relative to the GCM range of 0.23-3.62 (kgm-2)-1, where albedo is unitless. The overall constraint on the contribution of SO SWFB to global cloud feedback is -0.19-0.05 Wm-2K-1, relative to GCM range of -0.28-0.27 Wm-2K-1. In summary, observations suggest a moderate negative to weak positive SO SWFB.