The Denmark Strait plays an important role as a dense water gateway between the Arctic and the subpolar North Atlantic. Previous studies have shown that the volume transport over the sill is limited by hydraulic constraints. A regional ocean-circulation model (ROMS) with a horizontal resolution of ≈1/20¿ degree and 30 sigma layers in the vertical is applied to study the through flow characteristics for Last Glacial Maximum to Holocene conditions. The bathymetry of the gateway region is obtained from a geodynamic model that takes into account the differential ice loading of the adjacent continents. First, the upstream reservoir conditions are systematically changed to test hydraulic limitations for altered bathymetry. Generally, the through flow is less than the predicted maximal value from hydraulic theory by almost 50%. The results indicate that the reduction in gateway depth and aperture owing to glacial-isostatic processes alone lead to a considerable further reduction of the overflow, by approximately 33%, compared to the present day. Second, the through flow is modeled using average density profiles and wind stress from global model data. The reduction in the density-driven part of the overflow is partly compensated by an enhanced wind stress but is still reduced by a factor of 5. Owing to the narrowing of the strait during the glacial and the increased northerly wind, the North Icelandic Irminger Current was strongly reduced but still existent.