Present Doppler-spreading models for short internal waves in the atmosphere and the ocean either neglect the time dependence of the background long-wave shear entirely, or ignore time-dependent effects in their parametrization of dissipation. We use ray and numerical simulations to examine the Doppler spreading of a short internal-wave packet by an inertia-wave packet. The results are enough to show that time dependence in the long-wave shear can make a significant difference to short-wave behavior, and will need to be taken into account in future modelling efforts. ¿ 1997 American Geophysical Union