Damping in the contact of a rigid conical indenter with a viscoelastic half-space under superimposed normal and tangential oscillation is considered, with perfect sticking in the contact. The viscoelastic half-space is modeled with the Kelvin material. The energy dissipated per oscillation cycle is determined numerically in the framework of the method of dimensionality reduction (MDR). A particular focus of the present study is the influence of the changes in contact area due to the normal oscillation on the tangential component of dissipation.