Three experiments with an arithmetic working memory task examine the object switch effect first reported by Garavan (1998), which was interpreted as evidence for a focus of attention within working memory. Experiments 1a and 1b showed object switch costs with a task that requires selective access to items in working memory, but did not involve counting, and did not require updating of working memory contents, thus ruling out two alternative explanations of Garavan's results. Experiment 2 showed object switch costs with a task that required no selective access to working memory contents, but involved updating, thus providing evidence for a second component to the overall object switch costs. Further analyses revealed that the object switch cost increased with memory set size; that there were (smaller) switch costs when the switch was to an item of the same type; that repeating an arithmetic operation does not have the same effect as repeating the object it is applied to; and that object switching is not mediated by backward inhibition of the previously focused object.