RARE/TSE/FSE imaging is the most common brain sequence, but can be severely degraded by patient motion. While 2D navigated versions (PROPELLER) and motion-tracking approaches exist, they are not widely used. We introduced a data-consistency based retrospective method, TAMER, whereby the image and motion parameters are jointly estimated by minimizing data consistency error of a SENSE+motion forward model. We employ reduced modeling techniques which assess only a few targeted voxels at each step to make the large non-linear estimation problem computationally achievable. We demonstrate the approach to mitigating rotations in phantom and human scans in addition to previously reported translation mitigation.