Two-dimensional numerical-simulation techniques have been used to study fluid instability in laser-fusion pellets. Comparisons with analytic solutions in nonablating test cases show good agreement. Isentropic ablative accelerations exhibit growth rates 50%-100% of Rayleigh-Taylor values, while nonisentropic cases show suppressed growth. Design optimization has led to an impulsively accelerated, low-aspect-ratio shell which operates successfully with a surface perturbation of a few tens of angstroms.