Lithospheric thinning by mantle plumes is an important planetary heat transfer process resulting in the broad topographic uplift that characterizes the volcanic rises on Venus, the Tharsis rise on Mars, and several hotspot swells on Earth. We present a suite of time-dependent, three-dimensional numerical calculations of a plume impinging upon the lithosphere in a temperature-dependent viscosity mantle. Efficient lithospheric thinning is found to depend on the formation of convective instabilities in the plume-lithosphere boundary layer. These instabilities are non-axisymmetric, time-dependent, and have horizontal scales of a few tens of kilometers. These instabilities depend on the temperature-dependence of viscosity and occur when the plume's viscosity is about an order of magnitude less than the background mantle, as predicted by boundary-layer theory. Thus, in planetary mantles, plumes with excess temperatures of 100 to 200 K will efficiently thin the lithosphere via small-scale convective instabilities. ¿ 1999 American Geophysical Union