Overshadowing and blocking are two important findings that are frequently used to constrain models of associative learning. Overshadowing is the finding that learning about a cue (referred to as X) is reduced when that cue is always accompanied by a second cue (referred to as A) during the learning phase (AX). Blocking is the finding that after learning a stimulus-outcome relation for one stimulus (A), learning about a second stimulus (X) is reduced when the second stimulus is always accompanied by the first stimulus (AX). It remains unclear whether overshadowing and blocking result from explicit decision processes (e.g., “I know that A predicts the outcome, so I am not sure whether X does, too”), or whether cue competition is built directly into low-level association formation processes. In that vein, the present work examined whether overshadowing and/or blocking are present in an incidental learning procedure, where the predictive stimuli (words or shapes) are irrelevant to the cover task and merely correlated with the task-relevant stimulus dimension (colour). In two large online studies, we observed no evidence for overshadowing or blocking in this setup: (a) no evidence for an overshadowing cost was observed with compound (word-shape) cues relative to single cue learning conditions, and (b) contingency learning effects for blocked stimuli did not differ from those for blocking stimuli. However, when participants were given the explicit instructions to learn contingencies, evidence for blocking and overshadowing was observed. Together, these results suggest that contingencies of blocked/overshadowed stimuli are learned incidentally, but are suppressed by explicit decision processes due to knowledge of the contingencies for the blocking/overshadowing stimuli.