The transport of freshwater is analyzed in an eddy-permitting regional model of the sub-polar North Atlantic, focusing on the export of freshwater (in liquid form) through Davis Strait. The results show that in the model simulations there is a limited exchange of freshwater between the Labrador shelf and the interior of the Labrador Sea. Very little of the freshwater exported from the Canadian Arctic gets taken up into the model Labrador Sea water (6--8%). Enhancing the freshwater export through Davis Strait by 2/3s has little effect on the freshwater content in the Labrador Sea interior, as well as on Labrador Sea Water formation.