  Perturbative $\alpha '$ corrections to the low energy string effective action
have been recently found to have a potentially regularizing effect on the
singularity of the lowest order pre-big-bang solutions. Whether they actually
regularize it, however, cannot be determined working at any finite order in a
perturbative expansion in powers of the string constant $\alpha '$, because of
scheme dependence ambiguities. Physically, these corrections are dominated by
the integration over the first few massive string states. Very massive string
modes, instead, can have a regularizing effect which is non-perturbative in
$\alpha '$ and which basically comes from the fact that in a gravitational
field with Hubble constant $H$ they are produced with an effective Hawking
temperature $T=H/(2\pi)$, and an infinite production rate would occur if this
temperature exceeded the Hagedorn temperature. We discuss technical and
conceptual difficulties of this non-perturbative regularization mechanism.
