The reversal logical recoding rule (i.e., “respond opposite”) induced by an incompatible task (e.g., a task requiring to respond to red or green stimuli by pressing a key of the alternative colour compared to that of the stimulus) can be transferred to another task when the two tasks are combined in a task-switching paradigm. When the task to which the rule is transferred is a Simon task, this causes the disappearance of the typical advantage for responses that spatially correspond to the stimulus, or even results in an advantage for spatially noncorresponding responses. The present study aimed at investigating whether the transferred rule is independent of the specific stimulus and response dimensions for which it has been created. Previous studies suggest that when a Simon task is coupled with a colour incompatible task, the Simon effect may disappear or reverse even when stimuli in the two tasks, apart from being both visual and appearing on the same computer screen, have no other features in common. Results of the present study corroborate the hypothesis that feature overlap between stimuli is not necessary for the between-task transfer of the logical rule. However, an overlap between the representations of responses appears to be crucial. No modulation of the Simon effect was observed when the Simon task required bimanual responses while the colour-compatibility task required either vocal responses or responses executed with the two feet. In contrast, we did observe such a modulation when the discriminative response dimension and the effectors/response device were the same in the two tasks, even though these two tasks provided for different stimuli.