Our goal here is threefold: [1] To present a new dense-stereo matching algorithm, tMGM, that by combining the hierarchical logic of tSGM with the support structure of MGM achieves 6-8\% performance improvement over the baseline SGM (these performance numbers are posted under tMGM-16 in the Middlebury Benchmark V3 ); and [2] Through an exhaustive quantitative and qualitative comparative study, to compare how the major variants of the SGM approach to dense stereo matching, including the new tMGM, perform in the presence of: (a) illumination variations and shadows, (b) untextured or weakly textured regions, (c) repetitive patterns in the scene in the presence of large stereo rectification errors. [3] To present a novel DEM-Sculpting approach for estimating initial disparity search bounds for multi-date satellite stereo pairs. Based on our study, we have found that tMGM generally performs best with respect to all these data conditions. Both tSGM and MGM improve the density of stereo disparity maps and combining the two in tMGM makes it possible to accurately estimate the disparities at a significant number of pixels that would otherwise be declared invalid by SGM. The datasets we have used in our comparative evaluation include the Middlebury2014, KITTI2015, and ETH3D datasets and the satellite images over the San Fernando area from the MVS Challenge dataset.