The effect of ambient pressure on the intrinsic instability of rapid vaporization in single droplets boiling explosively at the limit of superheat has been studied experimentally and theoretically. The instability that distorts the evaporating interface and substantially enhances the mass flux at atmospheric pressure is suppressed at high pressure. The radiated pressure field is two orders of magnitude smaller from stabilized bubbles than from unstable. At intermediate pressures bubble growth occurs in two stages, first stable, then unstable. The Landau–Darrieus instability theory predicts absolute stability at atmospheric pressure for a spherical bubble, whereas the theory for planar interfaces yields results in general agreement with observation. The sensitivity of the instability to temperature suggests that small temperature nonuniformities may be responsible for quantitative departures of the behavior from predictions.