This paper presents methods for recovering accurate binocular disparity estimates in the vicinity of 3D surface discontinuities. Of particular concern are methods that impact coarse-to-fine, block matching as it forms the basis of the fastest and resource efficient disparity estimation procedures. Two advances are put forth. First, a novel approach to coarse-to-fine processing is presented that adapts match window support across scale to ameliorate corruption of disparity estimates near 3D boundaries. Second, a novel formulation of half-occlusion cues within the coarse-to-fine, block matching framework is described to inhibit false matches that can arise in regions near occlusions. Empirical results show that incorporation of these advances in coarse-to-fine, block matching reduces disparity errors by more than a factor of two, while performing little extra computation.