Depending on the application at hand, it is often desirable to constrain the wanted deformation. The idea is to incorporate higher level information about the expected deformation. We examine the most common constraints and show again that they may be conveniently phrased in a variational setting. As a consequence, all of discussed modules allow for fast implementations and may be combined in any favorable order. We discuss individual methods for various applications, including the registration of histological serial sections of a human brain.