We analyze the results from over 20 numerical experiments with a global ocean general circulation model (OGCM) under different present and last glacial maximum (LGM) surface boundary conditions. The model exhibits a large range of circulation strengths and patterns, including strong and deep overturning of North Atlantic Deep Water (NADW) under LGM boundary conditions. Parameterizations tuned for today's ocean and fixed atmospheric temperatures contribute to this failure. The experiments show a close relation between the NADW and Antarctic Bottom Water (AABW) overturning cells in the Atlantic. High transport in the NADW cell is associated with little or no transport of AABW. The strength of the AABW overturning cell depends sensitively on the treatment of sea ice in the Southern Ocean. An atmospheric energy balance model coupled with the OGCM allows a free response of the sea ice component. Because of the close link between NADW and AABW, the northern source of deep water must be relatively weak during the LGM. An ocean circulation consistent with paleoclimatic evidence only results when the surface salinity in the northern North Atlantic is reduced. The solution then shows a southward expansion of the Arctic domain and a southward shift of the deep water formation area in the North Atlantic. The glacial NADW is less dense than modern NADW, and AABW occupies a larger part of the abyssal ocean. Compared to modern distributions, there is almost no glacial Antarctic Intermediate Water causing middepth warming in the southern and tropical Atlantic.