Exponential weighting of future tracking errors and control increments is employed for receding-horizon predictive control and seen to improve the dynamic behaviour of the closed-loop system. A sufficient condition for the asymptotic stability ofgeneralized predictive control(GPC) with these weightings is derived. The condition can be easily satisfied whereas the corresponding condition for GPC with constant weighting is highly restrictive. In the case ofconstrained receding-horizon predictive control(CRHPC), a prescribed degree of stability is obtained just as with infinite-horizon optimal control using the same type of weighting. This makes it possible to use a simplified CRHPC law with no weighting on the tracking error but which guarantees convergence to the set-point faster than a bounding exponential