  We study the low-temperature properties of the classical three-dimensional
compass or $t_{2g}$ orbital model on simple-cubic lattices by means of
comprehensive large-scale Monte Carlo simulations. Our numerical results give
evidence for a directionally ordered phase that is reached via a first-order
transition at the temperature $T_0 = 0.098328(3) J / k_{\mathrm{B}}$. To obtain
our results we employ local and cluster update algorithms, parallel tempering
and multiple histogram reweighting as well as model-specific screw-periodic
boundary conditions, which help counteract severe finite-size effects.
