Abstract: Recently, generating a high quality all-hex mesh of a given volume has gained much attention. However, little, if any, effort has been put into the optimization of the hex-mesh structure, which is equally important to the local element quality of a hex-mesh that may influence the performance and accuracy of subsequent computations. In this paper, we present a first and complete pipeline to optimize the global structure of a hex-mesh. Specifically, we first extract the base-complex of a hex-mesh and study the misalignments among its singularities by adapting the previously introduced hexahedral sheets to the base-complex. Second, we identify the valid removal base-complex sheets from the base-complex that contain misaligned singularities. We then propose an effective algorithm to remove these valid removal sheets in order. Finally, we present a structure-aware optimization strategy to improve the geometric quality of the resulting hex-mesh after fixing the misalignments. Our experimental results demonstrate that our pipeline can significantly reduce the number of components of a variety of hex-meshes generated by state-of-the-art methods, while maintaining high geometric quality.