The height datum problem is present in the geodetic literature since the times of Pizzetti, when it was realized that as only differences of the gravity potential can be derived from measurements, there was still one global parameter to be settled in order to determine a global model. Several more realistic formulations of the problem have been introduced into the geodetic literature. After reviewing them, an ultimate formulation is attempted where only local data are given stemming from levelling, gravimetry, classical geodetic network observations, combined with global GPS-like observations. The problem of contemporaneous height datum/geodetic datum determination is shown to be solvable, in ellipsoidal approximation, only if the classical tide gauge and network orientation information is taken into account, specially if the local datum does not refer to very large areas, e.g. of continental size. In fact we will show that when this classical information is missing for the datum problem referring to a fairly small area, it becomes, for instance, impossible to distinguish between a ‘vertical’ shift of the local ellipsoid and a change of the potential of the geoid, i.e. the choice of a slightly different gravity equipotential surface.