This paper reports calculations of the growth of Rayleigh-Taylor instabilities (1) in the ablator-pusher region such as may be caused by irregularities in an electron beam, and (2) in the pusher-fuel interface, a problem common to all inertial confinement fusion targets. For the first case, it is found that long density gradient scale lengths and scattering of the beam by the target both stabilize the shorter-wavelength instabilities, which would otherwise grow most rapidly of all. In the second case, it is found that moderately-short-wavelength instabilities may not degrade the target performance as much as has previously been supposed.