Glassy dynamics of rigid molecules is still a matter of controversy: the physics behind the relaxation process at time scales faster than that ruled by the viscosity, the so called Johari-Goldstein process, is not known. In this work we unravel the mechanism of such a process by using a simple molecular model in which the centers of mass of the molecules are forming an ordered lattice, and molecular reorientation is performed by jumps between equilibrium orientations. We have studied the dynamics of simple quasi-tetrahedral molecules CBr(n)Cl(4-n), n = 0, 1, 2, in their monoclinic phases by means of dielectric spectroscopy and nuclear quadrupole resonance: the first technique allows to measure in a broad time scale but it is insensitive to molecular particularities, while the second has a restricted time window but senses the movement of each chlorine atom separately. The dynamic picture emerging from these techniques is that the secondary relaxation process is related to the different molecular surroundings around each nonequivalent atom of the molecule. Dynamical heterogeneities thus seem to be the cause of the secondary relaxation in this simple model of glass.