  We show that, in the presence of a string gas, simple higher-derivative
modifications to the effective action for gravity can lead to bouncing and
cyclic cosmological models. The modifications bound the expansion rate and
avoid singularities at finite times. In these models the scale factors can have
long loitering phases that solve the horizon problem. Adding a potential for
the dilaton gives a simple realization of the pre-big bang scenario. Entropy
production in the cyclic phase drives an eventual transition to a
radiation-dominated universe. As a test of the Brandenberger-Vafa scenario, we
comment on the probability of decompactifying three spatial dimensions in this
class of models.
