  In this Letter, we describe how a spectrum of entropic perturbations
generated during a period of slow contraction can source a nearly
scale-invariant spectrum of curvature perturbations on length scales larger
than the Hubble radius during the transition from slow contraction to a
classical non-singular bounce (the `graceful exit' phase). The sourcing occurs
naturally through higher-order scalar field kinetic terms common to classical
(non-singular) bounce mechanisms. We present a concrete example in which, by
the end of the graceful exit phase, the initial entropic fluctuations have
become negligible and the curvature fluctuations have a nearly scale-invariant
spectrum with an amplitude consistent with observations.
