A new semiclassical approach to implementing the mapping Hamiltonian formulation of nonadiabatic dynamics is presented. The approach involves using initial distributions of mapping oscillator variables that focus the sampling in such a way as to recover individual trajectory motion over the occupied state potential surface. The usual semiclassical implementation of the mapping Hamiltonian approach only recovers this feature after ensemble averaging. We test the approach on several model problems and show that it converges with very few trajectories compared to the usual approach. (C) 2003 American Institute of Physics.