With the increasing amount of patient information that is being collected today, the idea of using this information to inform future patient care has gained momentum. In many cases, this information comes in the form of medical images. Several algorithms have been presented to automatically segment these images, and to extract structures relevant to different diagnostic or surgical procedures. Consequently, this allows us to obtain large data-sets of shapes, in the form of triangular meshes, segmented from these images. Given correspondences between these shapes, statistical shape models (SSMs) can be built using methods like Principal Component Analysis (PCA). Often, the initial correspondences between the shapes need to be improved, and SSMs can be used to improve these correspondences. However, just as often, initial segmentations also need to be improved. Unlike many correspondence improvement algorithms, which do not affect segmentation, many segmentation improvement algorithms negatively affect correspondences between shapes. We present a method that iteratively improves both segmentation as well as correspondence by using SSMs not only to improve correspondence, but also to constrain the movement of vertices during segmentation improvement. We show that our method is able to maintain correspondence while achieving as good or better segmentations than those produced by methods that improve segmentation without maintaining correspondence. We are additionally able to achieve segmentations with better triangle quality than segmentations produced without correspondence improvement.