In this paper, we propose a novel method, which we call CONSISTENT ZOOMOUT, for efficiently refining correspondences among deformable 3D shape collections, while promoting the resulting map consistency. Our formulation is closely related to a recent unidirectional spectral refinement framework, but naturally integrates map consistency constraints into the refinement. Beyond that, we show further that our formulation can be adapted to recover the underlying isometry among near-isometric shape collections with a theoretical guarantee, which is absent in the other spectral map synchronization frameworks. We demonstrate that our method improves the accuracy compared to the competing methods when synchronizing correspondences in both near-isometric and heterogeneous shape collections, but also significantly outperforms the baselines in terms of map consistency.