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A recent paper proposed an MPC methodology which achieved a considerable reduction in the online optimization by transferring some of the computational load to calculations that can be performed offline. The approach was based on an augmented autonomous state space formulations of the prediction dynamics and gained significantly in efficiency by imposing a terminal constraint at current time. The approach was subsequently further extended with the view to improving the optimality of the approach by delaying the imposition of the terminal constraint by one prediction time instant. Over and above the computational advantages of the approach, it was demonstrated that the results were nearly optimal (e.g. to within 1% for 90% of all of the 2; 400 second order models simulated). However the simulations used, imposed a weight on the input, and it has been observed that performance deteriorates as the weight on the input in the prediction cost decreases. It is the purpose of the present paper to propose a further extension which removes this difficulty, yields further significant improvements on the degree of optimality, and achieves this at a modest extra computational cost.