In the present study, we examined how the relevance of potentially distracting information modulates the interplay of target and distractor processing in conflict tasks. Specifically, we manipulated the degree to which distracting information is relevant for performing the overall task by varying the proportion of trials in which a response to the distractor(s) (Experiments 1a and 1b: location in a Simon task; Experiment 2: flankers in an Eriksen flanker task) instead of to the target was required. Across all experiments, the congruency effect on mean RT was larger with the increasing relevance of the distractor(s). Critically, the slopes of the delta plot were more strongly increasing when the distractors were potentially relevant (as opposed to completely irrelevant), suggesting that cognitive control affects the timing of suppressing distractor-based activation. In addition, delta plot and diffusion model analyses revealed that the strength of suppressing distractor processing and the efficiency of target processing were enhanced when the distractors were less relevant. Overall, the present study dissociated multiple and time-dependent adjustments of control processes (i.e., target processing enhancement plus timing and strength of distractor suppression) in environments that encourage either a more stable or more flexible processing mode. (PsycInfo Database Record (c) 2023 APA, all rights reserved).