We report on our investigation of the Rayleigh-Taylor (R-T) and Kelvin-Helmholtz (K-H) instabilities in laser ablatively accelerated targets for single mode perturbations for a series of wavelengths in the parameter regime 1/2 less than or equal to lambda/delta R less than or equal to 10, where lambda is the wavelength of the perturbation and delta is the cold foil thickness. We find linear growth rates well below classical values (by a factor on the order of 3-4). We also find a cutoff in the growth rates for wavelengths less than the foil thickness. The striking result is the dominance of nonlinear effects; i.e., the K-H instability for short wavelength perturbations. Although the linear growth rates increase as k1/2 up to the cutoff, the K-H rollup dominates at large k, drastically reducing the penetration rate of the dense spike below its free fall value and effectively doubling the aspect ratio of the foil. In other words, it is the long wavelength perturbations that are most effective in destroying the symmetric implosion of the shell.