Matched-texture coding (MTC) exploits the redundancy of textured regions in natural images in order to achieve lowencoding-rate structurally lossless compression. A key element of MTC identifying large image blocks that can be replaced with previously encoded blocks that have similar structure. The side matching (SM) approach attempts to do this by matching the upper and left boundary (side) of a target block with the corresponding boundary of the candidate block, and then, among the best side matches, selecting the one that best matches the target block. We explore the effectiveness of, and interplay between, three SM criteria in order to increase the number and quality of matches and to reduce the computational complexity. The criteria are meansquared-error, log variance ratio, and partial implementations of STSIM-2, a recently proposed structural texture similarity metric. We propose a hierarchical algorithm for side matching, with three layers that utilize the three metrics, that improves performance and reduces the computation complexity. To set thresholds for the first and second layers of the hierarchical algorithm, we rely on Bayesian hypothesis testing. To estimate the necessary local probability densities, we introduce an adaptive estimation technique that depends on the side matching search region. Experimental results demonstrate an improvement of quality for a given encoding rate over previous realizations of MTC.