Geometric seismic attributes such as coherence are routinely used for highlighting geologic features such as faults and channels. Traditionally, we use a single user-defined analysis window of fixed size to calculate attributes for the entire seismic volume. In general, smaller windows produce sharper geologic edges, but they are more sensitive to noise. In contrast, larger windows reduce the effect of random noise, but they might laterally smear faults and channel edges and vertically mix the stratigraphy. The vertical and lateral resolutions of a 3D seismic survey change with depth due to attenuation losses and velocity increase, such that a window size that provides optimal images in the shallower section is often too small for the deeper section. A common workaround to address this problem is to compute the seismic attributes using a suite of fixed windows and then splice the results at the risk of reducing the vertical continuity of the final volume. Our proposed solution is to define laterally and vertical smoothly varying analysis windows. The construction of such tapered windows requires a simple modification of the covariance matrix for eigenstructure-based coherence and a less obvious, but also simple, modification of semblance-based coherence. We determine the values of our algorithm by applying it to a vintage 3D seismic survey acquired offshore Louisiana, USA.