A constrained minimum-variance prediction using self-tuning ideas is presented. Generalized cost functions are considered which penalize the prediction error as well as several choices of increments of prediction. It is claimed that constraining the prediction increments (or, differences in prediction) leads to more realistic and improved prediction strategies. The proposed formulations are developed on an ARIMAX process model, as it is believed that such a representation is more appropriate in practice. Various features are incorporated into the prediction algorithms to make them particularly suitable for real-time applications.