Abstract Recently developed seismic attributes such as volumetric curvature and amplitude gradients enhance our ability to detect lineaments. However, because these attributes are based on derivatives of either dip and azimuth or the seismic data themselves, they can also enhance high-frequency noise. Recently published structure-oriented filtering algorithms show that noise in seismic data can be removed along reflectors while preserving major structural and stratigraphic discontinuities. In one implementation, the smoothing process tries to select the most homogenous window from a suite of candidate windows containing the analysis point. A second implementation damps the smoothing operation if a discontinuity is detected. Unfortunately, neither of these algorithms preserves thin or small lineaments that are only one voxel in width. To overcome this defect, we evaluate a suite of nonlinear feature-preserving filters developed in the image-processing and synthetic aperture radar (SAR) world and apply them to both synthetic and real 3D dip-and-azimuth volumes of fractured geology from the Forth Worth Basin, USA. We find that the multistage, median-based, modified trimmed-mean algorithm preserves narrow geologically significant features of interest, while suppressing random noise and acquisition footprint.