  It is pointed out that massive states in D=4, N=1 supergravity-matter
theories can, in general, at the 1-loop level contribute non-holomorphic terms
to quadratic gravitational couplings. It is then shown in the context of
$(2,2)$-symmetric $Z_N$-orbifold theories that, for constant moduli
backgrounds, the inclusion of such contributions can result in the cancellation
of naked $C^2$-terms. ${\cal R}^2$-terms can also arise but, being ghost free,
need not cancel.
