In this work we formulate a control strategy for the control of a Wave Energy Converter (WEC) aiming to maximize power take off taking into account losses in the conversion from mechanical to electrical power. The analysis is based on a point absorber. Maximizing electrical power however results in large variations in the forces or torques in the structure implying large fatigue burden giving reduced life time or requirements for increased dimensions of the structure; therefore there is a tradeoff between harvested energy and demands to the construction. We suggest analysis of this involving a Model Predictive Control (MPC) strategy. Fatigue is usually assessed using the method of rainflow counting and Miner’s rule. This model is difficult to include in an MPC formulation, instead we chose to give torque in the shaft of the power take off a quadratic weight in the performance function and evaluate the fatigue from simulated results. The optimization of power take off relies on a model of losses in the power conversion. For the control we apply an approximated friction model. Simulations are performed using time-series of wave forms representing sea states typical for the intended location of the WEC. A Pareto front illustrates obtained mean power versus necessary dimensions due to fatigue. The results are compared with standard resistive and reactive controllers. The results show that the MPC produces more than 25 % more harvested energy than the reactive control for the same requirements for the dimensions.