  The simplest possible classical model leading to a cosmological bounce is
examined in the light of the non-Gaussianities it can generate. Concentrating
solely on the transition between contraction and expansion, and assuming
initially purely Gaussian perturbations at the end of the contracting phase, we
find that the bounce acts as a source such that the resulting value for the
post-bounce $f_{\mathrm{NL}}$ may largely exceed all current limits, to the
point of potentially casting doubts on the validity of the perturbative
expansion. We conjecture that if one can assume that the non-Gaussianity
production depends only on the bouncing behavior of the scale factor and not on
the specifics of the model examined, then many realistic models in which a
nonsingular classical bounce takes place could exhibit a generic
non-Gaussianity excess problem that would need to be addressed for each case.
