Direct model updating schemes modify the entries of system matrices to better match modal data. Thus far this has been done under the constraint imposed by symmetry and, in some cases, zeros from connectivity. Relations between coefficients of the stiffness matrix imposed by equilibrium, however, which are here designated as static constraints, have not been considered. The addition of static constraints to those from symmetry and connectivity completes the set of constraints and restricts the solution space of any direct update to that which is parametrically realizable from the model; eliminating, in this way, the long standing drawback of matrix modifications that have no physical interpretation. Static constraints lead to reductions in the amount of modal data needed to attain a unique solution and, as one anticipates, improve the accuracy of the update, in general.