Statistical models of deformations (SMD) capture the variability of deformations of a group of sample images, and they are often used to constrain deformable registration, thereby improving their robustness and accuracy. Although low- dimensional statistical models, such as active shape and appearance models, have been successfully used in statistically-constrained deformable models, constraining of high- dimensional warping algorithms is a more challenging task, since conventional PCA-based statistics are limited to capture the full range of anatomical variability. This paper first proposes an SMD that is built upon the wavelet-PCA model and then uses it to constrain the deformable registration, wherein the template image is adaptively warped based on SMD during the registration procedure. Compared to the original template image, the adaptively deformed template image is more similar to the subject image, e.g., the deformation is relatively small and local, and it is less likely to be stuck in undesired local minima. In experiments, we show that the proposed statistically-constrained deformable registration is more robust and accurate than the conventional registration.