Although domain-specificity is prevalent in models of human cognition, its presence is not always easy to verify. For example, according to one prominent model, experiencing conflict from an incongruent distractor in a Stroop-like task triggers an upregulation of domain-specific control that facilitates the resolution of the same, but not a different, type of conflict in the next trial. The only evidence for this view, however, comes from tasks wherein confounds can mimic the effects of domain-specific control. In the present study, I report that Stroop-incongruent and Simon-incongruent distractors in a hybrid Stroop-Simon task trigger selective reductions of the Stroop and Simon effects in the next trial (i.e., distractor-specific congruency sequence effects [CSEs]), regardless of whether confounds are absent (Experiment 1) or present (Experiment 2). However, I also report that the Stroop and Simon effects interact when confounds are absent (Experiment 1) and in trials with slow reaction times when confounds are present (Experiment 2). These within-trial interactions suggest that the Stroop and Simon effects index overlapping conflicts, rather than independent conflicts. Thus, they prevent one from drawing any conclusions about whether the distractor-specific CSEs index domain-specific (i.e., conflict-specific) or domain-general (i.e., conflict-general) control. This outcome challenges prior data suggesting domain-specific control in the hybrid Stroop-Simon task. However, it fits with recent findings suggesting independent within- and across-trial conflict control processes. It also fits with an emerging view wherein across-trial conflict control processes engender CSEs by retrieving an episodic memory of previous-trial control settings.