Random walker image registration has recently been extended in [1] to enforce inverse consistency in the solution by registering the input images towards a common space that resides midway between the two images. In this paper, we propose a novel extension to [1] to further improve its accuracy. We do so by proposing a voxel selection criterion that examines consistency of the data-likelihood estimates computed between the forward and backward directions. In particular, poor agreement occurs at locations where the top candidate displacement labels preferred by the forward direction conflict with those preferred by the backward direction. Once data-consistency is measured at every voxel location, the data-likelihood estimates of locations with low data-consistency are adjusted so that these nodes will contribute minimally to the similarity calculation. Experiments using different image modalities and image similarity measures show that this scheme can improve registration accuracy significantly per statistical analyses.