Harmonic surface deformation is a well-known geometric modeling method that creates plausible deformations in an interactive manner. However, this method is susceptible to artifacts, in particular close to the deformation handles. These artifacts often correlate with strong gradients of the deformation energy. In this work, we propose a novel formulation of harmonic surface deformation, which incorporates a regularization of the deformation energy. To do so, we build on and extend a recently introduced generic linear regularization approach. It can be expressed as a change of norm for the linear optimization problem, i.e., the regularization is baked into the optimization. This minimizes the implementation complexity and has only a small impact on runtime. Our results show that a moderate use of regularization suppresses many deformation artifacts common to the well-known harmonic surface deformation method, without introducing new artifacts.