We present a new technique for circumventing the problem of the zero-point leak in classical trajectories by extending the action-billiard approach of de Aguiar and Ozorio de Almeida [Nonlinearity 5, 523 (1992)]. In addition to demonstrating its utility in a model problem, we examine the application of various methods of overcoming the zero-point leak in the case of collinear He+H-2(+) collisions. We also show that not neglecting leaky trajectories gives, on an average, good agreement with quantal results for collinear as well as 3-dimensional collisions.