  We present a closed bouncing universe model where the value of coupling
constants is set by the dynamics of a ghost-like dilatonic scalar field. We
show that adding a periodic potential for the scalar field leads to a cyclic
Friedmann universe where the values of the couplings vary randomly from one
cycle to the next. While the shuffling of values for the couplings happens
during the bounce, within each cycle their time-dependence remains safely
within present observational bounds for physically-motivated values of the
model parameters. Our model presents an alternative to solutions of the fine
tuning problem based on string landscape scenarios.
