In the early seventies, a broad scientific debate began upon the nature of the conditions to be applied at the core-mantle interface in order to study the static deformations of the Earth. This controversy, which first arose in the context of post-seismic deformations, has also affected later investigations on inertia perturbations driven by surface or internal density contrasts. The aim of this communication is not to readdress the long-standing question about the appropriate set of boundary conditions to be imposed at the core-mantle boundary, but rather to show how the choice of these conditions may affect the calculation of inertia changes. When applied to glacially-induced inertia perturbations, our results demonstrate that the pitfall of the core-mantle boundary conditions has been acting for a long time after the scientific discussion mentioned above came to an end. ¿ American Geophysical Union 1995