Recently, Wang and Theeuwes (Journal of Experimental Psychology: Human Perception and Performance, 44(1), 13-17, 2018a) demonstrated the role of lingering selection biases in an additional singleton search task in which the distractor singleton appeared much more often in one location than in all other locations. For this location, there was less capture and selection efficiency was reduced. It was argued that statistical learning induces plasticity within the spatial priority map such that particular locations that are high likely to contain a distractor are suppressed relative to all other locations. The current study replicated these findings regarding statistical learning (Experiment 1) and investigated whether similar effects can be obtained by cueing the distractor location in a top-down way on a trial-by-trial basis. The results show that top-down cueing of the distractor location with long (1,500 ms; Experiment 2) and short stimulus-onset symmetries (SOAs) (600 ms; Experiment 3) does not result in suppression: The amount of capture nor the efficiency of selection was affected by the cue. If anything, we found an attentional benefit (instead of the suppression) for the short SOA. We argue that through statistical learning, weights within the attentional priority map are changed such that one location containing a salient distractor is suppressed relative to all other locations. Our cueing experiments show that this effect cannot be accomplished by active, top-down suppression. Consequences for recent theories of distractor suppression are discussed.