Gravitational, topographical and seismological studies of uplift regions around hot spots on oceanic,1,2 and continental plates3-7 have suggested that considerable lithospheric thinning has taken place beneath these areas. Previous models used to study this phenomenon have been based on thermal conduction8-11 and on the dynamic interaction between large-scale plume structures12 and the lithosphere, for a purely temperature-dependent viscosity. However, their predictions of the time scale for direct erosion12 of the lithosphere by these upwellings are too long. We propose here a new dynamical mechanism which works most efficiently for a temperature and pressure-dependent rheology. Our idea is that thinning of the lithosphere is accomplished by strong secondary convection enhanced by the presence of a low-viscosity zone which grows from a plume associated with a hot spot. This process is capable of producing the rapid time scale of the swell uplift13, of the order of 10 Myr, and the rates of thinning, of order 10 km Myr-1, required by both geophysical13,14 and geochemical15 observations.