  We study higher--derivative supergravity with curvature squared terms in
different bases. Performing a Weyl rescaling only on the metric or on all the
superfield components does not allow to obtain a normalized kinetic Einstein
term from a $\cR+\cR^2$ theory. It is necessary to combine a Legendre
transformation and a Weyl rescaling on a $\cR+\cR^2$ theory to arrive at a
theory of supergravity coupled to matter. This mechanism is applied to
supergravity coupled to a general function $k(R,\BR,\Phi,\bar\Phi)$, where $R$
is one of the supergravity chiral superfields and $\Phi$ a chiral matter
superfield.
