Most atmosphere-ocean general circulation models (GCMs) forced with increasing greenhouse gas concentrations predict enhanced atmospheric moisture transports to the high northern latitudes. Together with melting of Arctic sea ice and glaciers, this has led to the expectation of a gradual freshening of the northern North Atlantic, tending to reduce the strength of the Atlantic Meridional Overturning Circulation (AMOC). Here a multi-member greenhouse gas GCM experiment is used to demonstrate that both the salinity in the North Atlantic and the inflow of Atlantic Water to the Nordic Seas may increase despite a strong freshening of the Arctic Ocean and a reduced AMOC.