  We model the evolution of the abundances of light elements in carbon-enhanced
metal-poor (CEMP) stars, under the assumption that such stars are formed by
mass transfer in a binary system. We have modelled the accretion of material
ejected by an asymptotic giant branch star on to the surface of a companion
star. We then examine three different scenarios: one in which the material is
mixed only by convective processes, one in which thermohaline mixing is present
and a third in which both thermohaline mixing and gravitational settling are
taken in to account. The results of these runs are compared to light element
abundance measurements in CEMP stars (primarily CEMP-s stars, which are rich in
$s$-processes elements and likely to have formed by mass transfer from an AGB
star), focusing on the elements Li, F, Na and Mg. None of the elements is able
to provide a conclusive picture of the extent of mixing of accreted material.
We confirm that lithium can only be preserved if little mixing takes place. The
bulk of the sodium observations suggest that accreted material is effectively
mixed but there are also several highly Na and Mg-rich objects that can only be
explained if the accreted material is unmixed. We suggest that the available
sodium data may hint that extra mixing is taking place on the giant branch,
though we caution that the data is sparse.
