Quasiclassical trajectory calculations offer a cost-effective means of investigating the dynamics of chemical reactions. However, they suffer from the zero-point energy (ZPE) problem, whereby the (quantum) ZPE motion can contribute to an overestimation of the rate coefficient. This paper reports on some dynamics of the Henon-Heiles system. Dynamics of the water molecule at energies just below the (quantum) dissociation threshold, are also reported. The TRAPZ method [Lim and McCormack, J. Chem. Phys. 102, 1705 (1995)] leads to a definite improvement over unconstrained classical mechanics.