traction for Functional Languages with Control James Laird LFCS, Department of Computer Science University of Edinburgh This paper considers the consequences of relaxing the bracketing conditionon ‘dialoguegames’, showingthat this leads to a category of games which can be ‘factorized’ into a well-bracketed substructure, and a set of classically typed morphisms. These are shown to be sound denotations for control operators, allowing the factorization to be used to extend the definability result for PCF to one for PCF with control operators at atomic types. Thus we define a fully and effectively presentable model of a functional language with non-local control as part of a modular approach to modelling non-functional features using games.