The power output from wave-energy converters (WECs) may be increased by controlling the oscillation in order to approach an optimum interaction between the WEC and the incident wave. Optimally controlled WECs, designed to operate at full capacity a rather large fraction of their lifetime, may improve the economic prospects for wave power significantly. Most of the WECs discussed here utilise just one mode of oscillation. An upper bound is given to the ratio between the converted power from a given wave and the geometrical volume of the converter. One control strategy for maximising the converted power is based on measuring the incident wave, while another strategy utilises measurement of the WEC’s own oscillation as input to the controller. In either case, the measured quantity has to be predicted some seconds into the future because of noncausal control functions.