Terminal constraints in predictive control provide a guarantee stability, but result in deadbeat predicted responses and can violate physical constraints. Two recent algorithms (Rossiter ct al., 1996a; Scokaert and Rawlings, 1996) removed this restriction, but of these the former lacks the guarantee of l(2)-optimality whereas the latter lacks the guarantee of feasibility. Here we develop algorithms which overcome both these difficulties and illustrate their advantages by means of numerical examples.