The goal of the present study was to investigate the costs and benefits of different degrees of strategic parallel processing between two tasks. In a series of experiments with the dual-task flanker paradigm, participants were either instructed to process the tasks serially or in parallel, or—in a control condition—they received no specific instruction. Results showed that the participants were able to adjust the degree of parallel processing as instructed in a flexible manner. Parallel processing of the two tasks repeatedly led to large costs in performance and to high crosstalk effects compared to more serial processing. In spite of the costs, a moderate degree of parallel processing was preferred in the condition with no specific instruction. This pattern of results was observed if the same task set was used for the two tasks, but also if different ones were applied. Furthermore, a modified version of the central capacity sharing (CCS) model (Tombu and Jolicoeur in J Exp Psychol Hum Percept Perform 29:3–18,
2003) was proposed that accounts also for crosstalk effects in dual tasks. The modified CCS model was then evaluated by fitting it successfully to the present data.