Effective goal-directed behaviour requires not only selecting the correct response to stimuli in our environment, but also requires selection of the correct stimulus upon which to act. Many (but not all) studies of task switching require the selection and maintenance of mental representations of response options (so-called "response-sets"), but they do not require the selection and maintenance of mental representations of stimulus selection (so-called "stimulus-sets"). In the current experiments, a task switching paradigm was employed where the relevant stimulus-set (which stimulus to respond to) and response-set (how to respond to that stimulus) independently either repeated or switched. Central to the current investigation was to understand whether response-set and stimulus-set can be controlled independently, or whether they are bound together into a single representation. The theoretical framework of ECTVA (a computational model of dual-task control; Logan & Gordon, 2001) makes the strong claim that response-set and stimulus-set are unique control parameters that can updated independently. Predictions from ECTVA were used to design several experiments testing whether response-set and stimulus-set can be updated independently. All experiments confirmed ECTVA's predictions of an under-additive interaction between response-set and stimulus-set sequence, diagnostic of independent updating. However, limitations to this independent updating arose when participants were encouraged via preparation manipulations to selectively prioritise response-set or stimulus-set updating. The results are discussed in terms of other views on the structure of task-set representations, as well as how these representations are retrieved from memory to guide action.