Changes in water mass distribution are considered to be a significant contributor to the atmospheric CO2 concentration drop to around 186 ppm recorded during the Last Glacial Maximum (LGM). Yet simulating a glacial Atlantic Meridional Overturning Circulation (AMOC) in agreement with paleotracer data remains a challenge, with most models from previous Paleoclimate Modelling Intercomparison Project (PMIP) phases showing a tendency to simulate a strong and deep North Atlantic Deep Water (NADW) instead of the shoaling inferred from proxy records of water mass distribution. Conversely, the simulated Antarctic Bottom Water (AABW) is often reduced compared to its pre-industrial volume, and the Atlantic Ocean stratification is underestimated with respect to paleoproxy data. Inadequate representation of surface conditions, driving deep convection around Antarctica, may explain inaccurately simulated bottom water properties in the Southern Ocean. We investigate here the impact of a range of surface conditions in the Southern Ocean in the iLOVECLIM model using nine simulations obtained with different LGM boundary conditions associated with the ice sheet reconstruction (e.g., changes of elevation, bathymetry, and land–sea mask) and/or modeling choices related to sea-ice export, formation of salty brines, and freshwater input. Based on model–data comparison of sea-surface temperatures and sea ice, we find that only simulations with a cold Southern Ocean and a quite extensive sea-ice cover show an improved agreement with proxy records of sea ice, despite systematic model biases in the seasonal and regional patterns. We then show that the only simulation which does not display a much deeper NADW is obtained by parameterizing the sinking of brines along Antarctica, a modeling choice reducing the open-ocean convection in the Southern Ocean. These results highlight the importance of the representation of convection processes, which have a large impact on the water mass properties, while the choice of boundary conditions appears secondary for the model resolution and variables considered in this study.