Switching between tasks is assumed to be accompanied by inhibiting currently irrelevant, but competing tasks. A dominant task that strongly interferes with performing a weaker task may receive especially strong inhibition. We tested this prediction by letting participants switch among three tasks that differ in dominance: a location discrimination task with strong stimulus-response bindings (responding with left-hand and right-hand button presses to stimuli presented left or right to the fixation cross) was combined with a color/pattern and a shape discrimination task, for which stimulus-response mappings were arbitrary (e.g., left-hand button press mapped to a red stimulus). Across three experiments, the dominance of the location task was documented by faster and more accurate responses than in the other tasks. This even held for incompatible stimulus-response mappings (i.e., right-hand response to a left-presented stimulus and vice versa), indicating that set-level compatibility (i.e., "dimension overlap") was sufficient for making this location task dominant. As a behavioral marker for backward inhibition, we utilized n-2 repetition costs that are defined by higher reaction times for a switch back to a just abandoned and thus just inhibited task (ABA sequence) than for a switch to a less recently inhibited task (CBA, n-2 non-repetition). Reliable n-2 task repetition costs were obtained for all three tasks. Importantly, these costs were largest for the location task, suggesting that inhibition indeed was stronger for the dominant task. This finding adds to other evidence that the amount of inhibition is adjusted in a context-sensitive way.