Hydraulic constraints on the Denmark Strait overflow (DSO) are used as a parameterisation to improve the overflow representation in a global climate model. The parameterisation increases deep water formation in the Nordic Seas and strengthens the Norwegian Atlantic Current. Associated higher northward heat transport leads to a northward shift of the sea-ice edge and warming by 2.5¿C in the eastern Nordic Seas despite a small effect on the Atlantic Meridional Overturning Circulation (AMO). This emphasises the impact of the DSO on climate even though the response in overturning due to the DSO representation in this model is less than expected from previous studies using ocean only models. In contrast to previous studies almost no stabilising effect of the overflow on the AMO is found to freshwater perturbations.