A new model predictive control scheme with guaranteed stability is presented for constrained discrete-time nonlinear systems. The open-loop optimization problem does not involve explicit terminal constraints, and employs a nonstandard terminal cost function. The closed-loop system is shown to be infinite-horizon optimal, provided that the terminal cost exactly captures the infinite-horizon optimal value in a neighborhood of the origin. Stability and optimality are proven for a set of initial states, which is invariant and approaches the set of all controllable states, as the prediction horizon increases.