d abstract) John Longley Laboratory for Foundations of Computer Science School of Informatics, University of Edinburgh The King's Buildings, Mayfield Road Edinburgh EH9 3JZ, UK Abstract. We outline a general approach to providing intensional models for languages with computational effects, whereby the problem of interpreting a given effect reduces to that of finding an operator of higher type satisfying certain equations. Our treatment consolidates and generalizes an idea that is already implicit in the literature on game semantics. As an example, we work out our approach in detail for the case of fresh name generation, and discuss some particular models to which it applies.