  By demanding that a bounce is nonsingular and that perturbations are
well-behaved at all times, we narrow the scope of possible models with one
degree of freedom that can describe a bounce in the absence of spatial
curvature. We compute the general properties of the transfer matrix of
perturbations through the bounce, and show that spectral distortions of the
Bardeen potential $\Phi$ are generically produced only for the small
wavelengths, although the spectrum of long wavelength curvature perturbations
produced in a contracting phase gets propagated unaffected through such a
bounce.
