A new, fast, approximate quantum trajectory method was developed for solving multi-dimensional barrier transmission problems. The arbitrary Lagrangian-Eulerian (ALE) moving frame of reference was used, to avoid the isochrone search problem. Accurate transmission probabilities were found for wide-barrier problems using the 5th order Derivative Propagation Method (DPM). Real-valued trajectories were used both to carry flux to the barrier maximum, and to carry density to the transmitted side of the barrier, with correct results. Mixed results were found for other barrier cases and lower orders of the DPM. (C) 2009 Elsevier B.V. All rights reserved.