This work uses denotational models to understand and improve the part of a programming language concerned with non-local control operators. These operators let the programmer identify and restore arbitrary control contexts in the program execution path, and thus form a powerful component of many modern programming languages. We use a variety of denotational models to tackle the issues of (1) describing a control language mathematically, and (2) using the model's apparatus to obtain information useful for designing the language. For this, the full abstraction criterion of testing a model against a language is viewed as a feedback loop that suggests language changes. The results from radically different models, for a variety of control manipulation languages uniformly emphasize the need for delimiting control actions. In the case of higher-order control, this takes the form of a systematic handling of control objects. To check the pragmatics of the new control techniques, we present an implementation and many examples where these delimiters and handlers provide elegant solutions.