Exciting multiple-model (MM) estimation algorithms have a fixed structure, i.e., they use a fixed set of models. An important fact that has been overlooked for a long time is how the performance of these algorithms depends on the set of models used, Limitations of the fixed structure algorithms are addressed first. In particular, it is shown theoretically that the use of too many models is performance-wise as bad as that of too few models, apart from the increase in computation, This paper then presents theoretical results pertaining to the two ways of overcoming these limitations : select/construct a better set of models and/or use a variable set of models. This is in contrast to the existing efforts of developing better implementable fixed structure estimators. Both the optimal MM estimator and practical suboptimal algorithms with variable structure are presented. A graph-theoretic formulation of multiple-model estimation is also given which leads to a systematic treatment of model-set adaptation and opens up new avenues for the study and design of the MM estimation algorithms, The new approach is illustrated in an example of a nonstationary noise identification problem.