  We study a process of slow mixing in stars with convective envelopes, which
is driven by the settling of cool downward plumes below the base of the
convection zone. If a small fraction (of order $10^{-7}$) of the material
cooled at the surface retains a significant entropy deficit while descending in
plumes, it can reach the depth where lithium burning takes place. The model
calculates the thermal response and mixing below the convection zone due to the
settling process, assuming that the plumes arrive at the base of the convection
zone with a broad range of entropy contrasts. We obtain a good fit to the
observed lithium depletion in the Sun by assuming that the settling mass flux
is distributed with respect to the entropy contrast as a power law with a slope
around -2. We find convective settling to have a negligible influence on the
stratification below the convection zone, although mixing induced by it could
modify the gradient of helium concentration.
