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Large system dimensions and/or a possible need for long horizons restrict the applicability of predictive control. Earlier work showed that by sacrificing a certain degree of optimality it is possible to define efficient algorithms which reduce considerably computational complexity. This note considers a class of such algorithms which deploy just one degree of freedom. It is shown that it is possible to: (1) derive a priori stability guarantees over much larger regions of the state space and for a larger class of control trajectories; (2) account for a particular class of model uncertainty; and (3) show that even though a use is made of ellipsoidal invariant sets, nevertheless the stability results are not limited to the volume of such ellipsoids.