We propose a new numerical method for evaluating long-maturity American put options. Most existing numerical approaches are based on the time discretization of the exercise strategy, and their con- vergence to continuous exercise opportunities is very slow. Instead of assuming a nite number of exercise dates, we allow the option holder to exercise continuously, using an optimal barrier approach combined with a cubic spline interpolation technique. Our method is shown to converge to the American option price much more quickly than the Bermudian approximation, making it especially appropriate for long-maturity options.