Noise suppression of airborne gravity-gradiometer data is a crucial part of the data processing stream. We considered two approaches to removing noise: kriging and directional filtering. Kriging is an estimation procedure for the interpolation of spatial data. The estimator is calculated from the data variogram, which characterizes the noise level and correlation length of the measurements. Directional filtering uses a user-defined operator that is oriented to preferentially smooth the data along the strike, but it leaves short-wavelength components in the cross-strike direction for definition of the trend edges. Both methods were applied to a recently collected offshore gravity gradient survey. The kriging and directional filtering results revealed a similar level of smoothness, but the main difference between them was the extra smoothing along the strike for the directionally filtered data. Because kriging is a data-driven procedure, it provides an objective estimate of the data noise level and degree of smoothness. The processing parameters required for directional filtering can then be chosen to give a similar level of smoothness and noise suppression to the kriging results, but with the added advantage of directional smoothing, which more effectively delineates geologic trends in the data.