Seismic coherence is widely used in seismic interpretation and reservoir characterization to highlight (with low values) faults and stratigraphic features from a seismic image. A coherence image can be computed from the eigenvalues of conventional structure tenors, which are outer products of gradients of a seismic image. I have developed a simple but effective method to improve such a coherence image by using directional structure tensors, which are different from the conventional structure tensors in only two aspects. First, instead of using image gradients with vertical and horizontal derivatives, I use directional derivatives, computed in directions perpendicular and parallel to seismic structures (reflectors), to construct directional structure tensors. With these directional derivatives, lateral seismic discontinuities, especially those subtle stratigraphic features aligned within dipping structures, can be better captured in the structure tensors. Second, instead of applying Gaussian smoothing to each element of the constructed structure tensors, I apply approximately fault- and stratigraphy-oriented smoothing to enhance the lateral discontinuities corresponding to faults and stratigraphic features in the structure tensors. Real 3D examples show that the new coherence images computed from such structure tensors display much cleaner and more continuous faults and stratigraphic features compared with those computed from conventional structure tensors and covariance matrices.