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Controller-design issues influence modeling decisions; therefore, the modeling and controller-design problems are coupled. This paper proposes a quantification of this coupling in terms of the size of the set of models from which satisfactory controllers may be derived. Moreover, in the context of an extremely general framework, we prove that the coupling increases as performance specifications are tightened and as uncertainty is increased. Furthermore, the existence of a preferred model for controller design is demonstrated: this model is preferred in the sense that its use leads to improved robustness or performance. However, this model does not necessarily satisfy our intuitive notion of a worst-case model: rather, it depends on the performance specifications and uncertainty.