We study, numerically and experimentally, the momentum distribution of atoms
cooled in optical lattices. Using semi-classical simulations, we show that this
distribution is bimodal, made up of a central feature corresponding to "cold",
trapped atoms, with tails of "hot", untrapped atoms, and that this holds true
also for very shallow potentials. Careful analysis of the distribution of
high-momentum untrapped atoms, both from simulations and experiments, shows
that the tails of the distribution does not follow a normal law, hinting at a
power-law distribution and non-ergodic behavior. We also revisit the phenomenon
of d\'ecrochage, the potential depth below which the temperature of the atoms
starts increasing