  We show that the only Tolman models which permit a Vaidya limit are those
having a dust distribution that is hollow - such as the self-similar case. Thus
the naked shell-focussing singularities found in Tolman models that are dense
through the origin have no Vaidya equivalent. This also casts light on the
nature of the Vaidya metric. We point out a hidden assumption in Lemos'
demonstration that the Vaidya metric is a null limit of the Tolman metric, and
in generalising his result, we find that a different transformation of
coordinates is required.
