  We investigate both analytically and numerically the evolution of scalar
perturbations generated in models which exhibit a smooth transition from a
contracting to an expanding Friedmann universe. We find that the resulting
spectral index in the late radiation dominated universe depends on which of the
$\Psi$ or \$zeta$ variables passes regularly through the transition. The
results can be parameterized through the exponent $q$ defining the rate of
contraction of the universe. For $q \geq -1/2$ we find that there are no stable
cases where both variables are regular during the transition. In particular,
for $0<q\ll 1$, we find that the resulting spectral index is close to scale
invariant if $\Psi$ is regular, whereas it has a steep blue behavior if $\zeta$
is regular. We also show that as long as $q\leqslant 1$, perturbations arising
from the Bardeen potential remain small during contraction in the sense that
there exists a gauge in which all the metric and matter perturbation variables
are small.
