This paper explores optimal damping profiles for a heaving buoy wave energy converter (WEC). The approach is mathematical and the model of Eidsmoen (1995) is used as a basis. In order to permit analytical development, the model is initially simplified and an optimal damping profile is determined using numerical optimization. Having found the optimal damping profile, a semi-analytical solution methodology is developed to determine the optimal damping parameters. Finally, the procedure is validated on the original model and some aspects related to the control problem are addressed