  Listing has recently extended results of Kozameh, Newman and Tod for
four-dimensional spacetimes and presented a set of necessary and sufficient
conditions for a metric to be locally conformally equivalent to an Einstein
metric in all semi-Riemannian spaces of dimension n>3 -- subject to a
non-degeneracy restriction on the Weyl tensor. By exploiting dimensionally
dependent identities we demonstrate how to construct two alternative versions
of these necessary and sufficient conditions which we believe will be useful in
applications. The four-dimensional case is discussed in detail and examples are
also given in five and six dimensions.
