In this article, we employ a recently discovered criterion for selecting important contributions to the semiclassical coherent state propagator [T. Van Voorhis and E. J. Heller, Phys. Rev. A 66, 050501 (2002)] to study the dynamics of many dimensional problems. We show that the dynamics are governed by a similarity transformed version of the standard classical Hamiltonian. In this light, our selection criterion amounts to using trajectories generated with the untransformed Hamiltonian as approximate initial conditions for the transformed boundary value problem. We apply the new selection scheme to some multidimensional Henon-Heiles problems and compare our results to those obtained with the more sophisticated Herman-Kluk approach. We find that the present technique gives near-quantitative agreement with the the standard results, but that the amount of computational effort is less than Herman-Kluk requires even when sophisticated integral smoothing techniques are employed in the latter. (C) 2003 American Institute of Physics.