Recent geoids from the Gravity Recovery and Climate Experiment (GRACE) and the Gravity field and steady state Ocean Circulation Explorer satellite mission (GOCE) contain useful short-scale information for the construction of a geodetic ocean mean dynamic topography (MDT). The geodetic MDT is obtained from subtracting the geoid from a mean sea surface (MSS) as measured by satellite altimetry. A gainful use of the MDT and an adequate assessment needs an optimal filtering. This is accomplished here by defining a cutoff length scale dmax for the geoid and applying a Gaussian filter with half-width radius r on the MDT. A series of MDTs (GRACE, GOCE, and combined satellite-only (GOCO) solutions) is tested, using different sets of filter parameters dmax and r. Optimal global and regional dependent filter parameters are estimated. To find optimal parameters and to assess the resulting MDTs, the geostrophic surface currents induced by the filtered geodetic MDT are compared to corrected near-surface currents obtained from the Global Drifter Program (GDP). The global optimal cutoff degree and order (d/o) dmax (half-width radius r of the spatial Gaussian filter) is 160 (1.1°) for GRACE; 180 (1.1–1.2°) for 1st releases of GOCE (time- and space-wise methods) and GOCO models; and 210 (1.0 degree) for 2nd and 3rd releases of GOCE and GOCO models. The cutoff d/o is generally larger (smaller) and the filter length smaller (larger) for regions with strong, small-scale (slow, broad scale) currents. The smallest deviations from the drifter data are obtained with the GOCO03s geoid model, although deviations of other models are only slightly higher.