Despite the improvement in global geoid determination that the Gravity Recovery and Climate Experiment (GRACE) satellite mission has provided, it remains necessary to filter the ocean'smean dynamic topography (MDT) that is derived fromit to remove residual noise. A standard approach is to use isotropic spatial smoothing. Unfortunately, this also attenuatesMDT gradients associated with surface currents. Here an alternative, anisotropic approach taken from the field of image processing that preferentially filters along rather than across gradients is presented. Applying the method to theMDT of the North Atlantic, it is found that attenuation ofMDT gradients corresponding to important currents such as the Gulf Stream and Labrador Current ismuch reduced.Along the axis of theGulf Stream, this translates in places to more than a doubling in the estimated current speed compared to a conventionally filtered MDT.