We have used crosscorrelation, semblance, and eigenstructure algorithms to estimate coherency. The first two algorithms calculate coherency over a multiplicity of trial time lags or dips, with the dip having the highest coherency corresponding to the local dip of the reflector. Partially because of its greater computational cost, our original eigenstructure algorithm calculated coherency along an implicitly flat horizon. Although generalizing the eigenstructure algorithm to search over a range of test dips allowed us to image coherency in the presence of steeply dipping structures, we were somewhat surprised that this generalization concomitantly degenerated the quality of the fault images in flatter dip areas. Because it is a local estimation of reflector dip (including as few as five traces), the multidip coherency estimate provides an algorithmically correct, but interpretationally undesirable, estimate of the best apparent dip that explained the offset reflectors across a fault. We ameliorate this problem using two methods, both of which require the smoothing of a locally inaccurate estimate of regional dip. We then calculate our eigenstructure estimate of coherency only along the dip of the reflector, thereby providing maximum lateral resolution of reflector discontinuities. We are thus both better able to explain the superior results obtained by our earliest eigenstructure analysis along interpreted horizon slices, yet able to extend this resolution to steeply dipping reflectors on uninterpreted cubes of seismic data.