In continuously stratified fluid, vertically propagating internal gravity waves of moderately large amplitude can become unstable and possibly break due to a variety of mechanisms including (with some overlap) modulational instability, parametric subharmonic instability (PSI), self-acceleration, overturning, and convective instability. In PSI, energy from primary waves is transferred, for example, to waves with half frequency. Self-acceleration refers to a mechanism whereby a wave packet induces a mean flow (analogous to the Stokes drift of surface waves) that itself advects the waves until they become convectively unstable. The simulations presented here show that self-acceleration dominates over parametric subharmonic instability if the wave packet has a sufficiently small vertical extent and sufficiently fast frequency.