The Last Glacial Maximum (LGM, ~21k BC) was characterized by a cold and well-stratified ocean as documented by many proxy data from marine sediment cores, representing a benchmark test-bed for climate models. Even though much effort was made to reproduce the glacial ocean structure and associated large-scale ocean circulation, it remains difficult to reconcile the spread between models and mismatches to data. Here we employ a fully comprehensive climate model to explore the role of the ocean stratification on the Atlantic meridional overturning circulation (AMOC). Using glacial boundary conditions we find two states for the glacial ocean structure, depending on differences in the initial salinity stratification. Only one of the two ocean states is in agreement with the available proxy record. However, this state cannot be generated with LGM boundary conditions, implying a quasi steady nature of the glacial ocean water mass configuration. Furthermore, we show that the salinity stratification represents a key control on the spatial configuration and the strength of the AMOC and therefore bears the potential to reconcile the apparent differences among models and data. In combination these findings represent a new dynamical framework for AMOC changes on glacial-interglacial timescales that challenges the conventional evaluation of glacial and deglacial AMOC changes based on an ocean state derived from LGM boundary conditions.