Data regularization by azimuthal moveout (AMO) is an important seismic processing step applied to minimize the deleterious effects of irregular and incomplete acquisition in complex geology. Using isotropic AMO operators on data acquired over azimuthally anisotropic media, though, can lead to poor regularization results due to mixing of wavefield information from neighboring traces with azimuthally varying velocity profiles. An elliptical moveout operator (EMO), representing an extension of isotropic AMO to elliptical azimuthally anisotropic media, is sensitive to variations in the magnitude and the orientation of velocity ellipticity. AMO and EMO operators can be applied to regularize data by moving wavefield information from traces acquired at neighboring offsets and midpoints to infill existing data holes. Unlike AMO, though, EMO operators also can be used in a data conditioning procedure to interpolate energy between seismic traces where input and output velocity profiles are azimuthally elliptical and isotropic, respectively. Resulting processed data volumes are approximately free of elliptical azimuthal anisotropy, as can be shown by comparing analytical traveltimes and numerically calculated wavefield arrivals. EMO thus represents a one-step regularization/conditioning procedure for elliptically azimuthally anisotropic media that is more consistent with wave-equation physics and yields more accurate results than when compared with those from isotropic processing and elliptical residual moveout operator static corrections.