In this paper we propose a new method for non-rigid registration of PET/CT datasets incorporating prior knowledge about the rigidity of regions within the PET volumes into the matching process. State-of-the-art medical image registration approaches usually assume that the whole image domain is associated with a homogeneous deformation property, thus bone structure and soft tissue have the same stiffness, for instance. This assumption, however, is invalid in the majority of cases. In many applications the deformation properties can be estimated automatically by a segmentation step, beforehand. The presented non-rigid registration method integrates knowledge about the tissue directly into the deformation field computation. For this reason, no additional post-processing steps, like filtering of the deformation field, are required. To integrate the tissue constraints the regularizer is replaced by a novel spatially dependent smoother. Dependent on the location within the image, the smoother is able to explicitly adjust the rigidity. Thus, different tissue classes can be treated in the registration process. To pass the stiffness coefficients to the algorithm an additional mask image is used. The registration results are illustrated on synthetic data first to give a good intuition about the effectiveness of the proposed method. Finally, we illustrate the improvement of the registration using real clinical data. It is shown that the mono-modal registration of PET images yields more reasonable results using a spatially dependent regularizer constraining the deformations of regions with high tracer concentration than using a normal curvature regularizer. Furthermore, the method is evaluated on multi-modal PET/CT registration problems.