We investigate in this paper the sensitivity of the representation of the Denmark Strait overflow produced by a regional z-coordinate configuration of NEMO (version 3.6) to the horizontal and vertical grid resolutions and to various numerical and physical parameters. Three different horizontal resolutions, 1/12, 1/36, and 1/60 degrees, are respectively used with 46, 75, 150, and 300 vertical levels. In the given numerical set-up, the increase in the vertical resolution did not bring improvement at eddy-permitting resolution (1/12 degrees). We find a greater dilution of the overflow as the number of vertical level increases, and the worst solution is the one with 300 vertical levels. It is found that when the local slope of the grid is weaker than the slope of the topography the result is a more diluted vein. Such a grid enhances the dilution of the plume in the ambient fluid and produces its thickening. Although the greater number of levels allows for a better resolution of the ageostrophic Ekman flow in the bottom layer, the final result also depends on how the local grid slope matches the topographic slope. We also find that for a fixed number of levels, the representation of the overflow is improved when horizontal resolution is increased to 1/36 and 1/60 degrees, with the most drastic improvements being obtained with 150 levels. With such a number of vertical levels, the enhanced vertical mixing associated with the step-like representation of the topography remains limited to a thin bottom layer representing a minor portion of the overflow. Two major additional players contribute to the sinking of the overflow: the breaking of the overflow into boluses of dense water which contribute to spreading the overflow waters along the Greenland shelf and within the Irminger Basin, and the resolved vertical shear that results from the resolution of the bottom Ekman boundary layer dynamics. This improves the accuracy of the calculation of the entrainment by the turbulent kinetic energy mixing scheme (as it depends on the local shear) and improves the properties of the overflow waters such that they more favourably compare with observations. At 300 vertical levels the dilution is again increased for all horizontal resolutions. The impact on the overflow representation of many other numerical parameters was tested (momentum advection scheme, lateral friction, bottom boundary layer parameterization, closure parameterization, etc.), but none had a significant impact on the overflow representation.