The overflow of the dense water mass across the Greenland–Scotland Ridge (GSR) from the Nordic Seas drives the Atlantic meridional overturning circulation (AMOC). The Nordic Seas is a large basin with an enormous reservoir capacity. The volume of the dense water above the GSR sill depth in the Nordic Seas, according to previous estimates, is sufficient to supply decades of overflow transport. This large capacity buffers overflow’s responses to atmospheric variations and prevents an abrupt shutdown of the AMOC. In this study, the authors use a numerical and an analytical model to show that the effective reservoir capacity of the Nordic Seas is actually much smaller than what was estimated previously. Basin-scale oceanic circulation is nearly geostrophic and its streamlines are basically the same as the isobaths. The vast majority of the dense water is stored inside closed geostrophic contours in the deep basin and thus is not freely available to the overflow. The positive wind stress curl in the Nordic Seas forces a convergence of the dense water toward the deep basin and makes the interior water even more removed from the overflow-feeding boundary current. Eddies generated by the baroclinic instability help transport the interior water mass to the boundary current. But in absence of a robust renewal of deep water, the boundary current weakens rapidly and the eddy-generating mechanism becomes less effective. This study indicates that the Nordic Seas has a relatively small capacity as a dense water reservoir and thus the overflow transport is sensitive to climate changes.