  We present a significant improvement to a time-dependent WKB (TDWKB)
formulation developed by Boiron and Lombardi [JCP {\bf108}, 3431 (1998)] in
which the TDWKB equations are solved along classical trajectories that
propagate in the complex plane. Boiron and Lombardi showed that the method
gives very good agreement with the exact quantum mechanical result as long as
the wavefunction does not exhibit interference effects such as oscillations and
nodes. In this paper we show that this limitation can be overcome by
superposing the contributions of crossing trajectories. We also demonstrate
that the approximation improves when incorporating higher order terms in the
expansion. These improvements could make the TDWKB formulation a competitive
alternative to current time-dependent semiclassical methods.
