Finite element models are based upon known physical characteristics. But there are two main sources of error, namely (i) ill-defined joints and boundary constraints, and (ii) overstiffening due to the application of shape function discretization. It is difficult to correct an ill-defined constraint without simultaneously compensating (to some unknown degree) for discretization overstiffening. A general approach is proposed whereby the measured eigendata from a physical system are altered to resemble the eigendata of a discrete system with identical (but unknown) constraints. With the effects of discretization overstiffening present in both the adjusted measurements and the model it is straightforward to obtain progressively improved estimates of the constraint stiffnesses by using the least-squares method. The proposed approach may be considered to be equivalent to a model reduction scheme. Specific methods are applied to the correction of a stiffness in the joint of a finite element framework model.