This work presents, for the first time, a general mechanism of a rhombohedral (R)-triclinic (T) phase transition in Chevrel Phases (CPs) with small cations (radius < 1 Å), which was unclear in spite of intensive studies of these important materials in the past. In contrast to previous interpretation of the R ⇔ T transition in some CPs as cation ordering, T-distortion is regarded here as a particular case of general adaptation of the framework to cation insertion, which includes the deformations of the coordination polyhedra and their tilting. The research is based on a combination of experimental studies (in-situ neutron diffraction at different temperatures) for one model compound, MgMo6Se8, and structural analysis for a variety of known CPs. This analysis shows that the structure flexibility is fundamentally different for the R and T forms. As a result of the lower flexibility, in the R form, a strict correlation exists between the compression of the framework along the -3 symmetry axis and the cation position in the structure (the so-called 'derealization'). The decreasing derealization in the R-CPs, which occurs on cooling, leads to excessive repulsion within the cations pairs (R-Cu1.8Mo6S8 case) or undesirable asymmetry in the cation polyhedra (R-MgMo6-Se8 case). The higher flexibility of the T framework allows for relaxation of these structural strains by increasing the cation-cation distances and forming a more symmetric cation environment, sometimes with higher coordination number (CN), like CN = 5 in the T-Fe2Mo6S8 type. Thus, this work also proposes possible driving forces for T-distortion in CPs.