Long-range predictive control appears to be a better foundation for self-tuning compared withk-step ahead or model-reference approaches. Various methods have been proposed in the literature based on weighting-sequence models, and the paper unifies their development. By assuming a noise structure which involves Brownian motion, natural integrating action is achieved as opposed to thead hocapproaches previously used. Simulation studies using truncated models show that large numbers of parameters are necessary using weighting sequences, although a parallel method using a CARIMA model is entirely satisfactory. When used with nonminimum-phase plant, the dynamic matrix control method works best.