According to the comparator hypothesis (Miller & Matzel, 1988), cue competition depends on the association between a target stimulus (X) and a competing cue (e.g., an overshadowing cue [A]). Thus, it was expected that overshadowing would be reduced by establishing an inhibitory-like relationship between X and A before compound conditioning. In three lever press suppression experiments with rats, this expectation was supported. Experiment 1 showed that establishing an inhibitory X-A relationship reduced overshadowing. In Experiment 2, degrading the inhibitory-like relationship before conditioning allowed reinforced AX compound trials to result in overshadowing. Experiment 3 replicated the results of Experiment 2 when the inhibitory relationship was degraded after compound conditioning. The results support the view that within-compound associations are necessary not only for retrospective revaluation, but also for conventional cue competition.