This article presents a closed-form solution to the computation of unbalance correction masses for rigid rotors mounted on flexible bearings. The solution requires measurements of the response of the rotor-bearing system to the unbalance that is to be corrected, as well as knowledge of its total mass or other stiffness or damping parameters that are readily deducible from the mounting configuration. No detailed mathematical models or information from previous balancing runs are required. The computation is based on the relationships that exist between some spatial and modal parameters of rotor-bearing systems. Such relationships are derived in this article, and their use in the computation of balancing masses is presented and verified with results from an experimental test rig. This work demonstrates the feasibility of balancing rigid rotors without trial runs, detailed models or historical balancing records.