Two methods are explored for evolving wavefunctions using short-time propagators of Herman-Kluk form [M.F. Herman, E.K. Kluk, Chem. Phys. 91 (1984) 271], At each lime step the wavefunction is expanded in a set of coherent states distributed hi phase space about a guiding trajectory. A harmonic approximation for the potential allows the stability analysis to be done analytically. A Monte Carlo 'path integral' form for the long-time propagator is derived and tested for a simple harmonic system. Another approach, where the entire wavefunction is evolved one step at time, is applied to wavepacket motion in a Morse potential.