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This paper discusses wave-by-wave near-optimal control of a wave energy device in irregular waves. A deterministic propagation model is used to predict the wave elevation several seconds into the future at the device location. Two prediction approaches are considered. The first is based on a time series being measured over an advancing time window at a particular up-wave location. This approach is here utilized in long-crested irregular waves. The second approach uses successive snapshots of wave elevation measurements over an up-wave area. This approach is found more convenient for multi-directional waves, and is here applied in a bi-directional wave irregular wave field. A small, heaving vertical cylinder reacting against a deeply submerged (i.e. assumed to undergo negligible oscillations) mass is studied under wave-by-wave control. The non-causal feedforward control force required for optimum velocity under a swept-volume constraint is based on the past, current, and predicted wave elevation at the device. Results for time-averaged converted power and displacement/force maxima are obtained for a range of irregular wave conditions. Also presented in addition are energy conversion results with a feedback-alone control force using a multi-resonant control technique.