Switching between tasks necessitates maintaining tasks in high readiness, yet readiness creates paradoxical interference from these tasks when they are not currently required. “Optimal suppression”, which targets just the interfering information, provides a partial solution to this paradox. By examining the carryover of suppression of a competitor stimulus–response (S–R) set from Trial N − 1 to Trial N, Meiran, Hsieh and colleagues (Meiran et al., J Exp Psychol Learn mem cognit 36:992–1002, 2010; Cognit Affect Behav Neurosci 11:292–308, 2011, and Hsieh et al., Acta Psychol 141:316–321, 2012) found that only the competing stimulus–response (S–R) set of rules is suppressed. Specifically, they found that a competitor S–R set in Trial N − 1 incurs cost when it becomes the relevant set in Trial N [competitor becomes relevant (CbR)]. Extending this logic, we predicted performance benefit when the competitor S–R set in Trial N − 1 remains the competitor S–R set in Trial N [competitor remains competitor (CrC)]. Here, we examined the question of whether what is being suppressed when encountering a response conflict is the entire S–R set of rules (e.g., “IF pink PRESS right”, and “IF blue PRESS left”) or an even more specific representation, namely, the currently interfering S–R rule (e.g., just “IF blue PRESS left”). We show that both CbR and CrC interact with Response (i.e., left or right key), suggesting that the system can recognize the exact source of interference (the competing S–R rule), and inhibit only this source.