Nominal models of linear systems subject to uncertainty are normally assumed to be most representative of the class of all possible models and are used for the purposes of design. However, in general the controllers derived do not have acceptable properties with respect to robust stability and relative stability. The question then arises as to whether design should be based on models other than the nominal. In this paper, we consider this problem in the context of stable generalized predictive control and give a characterization of all models that lead to controllers with guaranteed robustness properties. A procedure for selecting a particular controller is given and the results are illustrated by numerical examples. These demonstrate very clearly that small amounts of detuning with respect to the response of the nominal model afford very significant gains by way of robustness.