Do people avoid visual distraction by suppressing locations expected to contain potent distractors? To address this issue, we combined a spatial cueing paradigm with a capture-probe paradigm. Each search display contained six shapes, two of which had the target shape. To know which target shape to respond to, participants had to use a spatial cue indicating the to-be-ignored locations for that trial. There were also two neutral locations that never contained distractors and so did not need to be suppressed, which served as a baseline. To assess spatial suppression below baseline, participants performed a probe letter recall task on 30% of trials. If people proactively suppress the threatening to-be-ignored locations below baseline, then probe recall for these cued-to-be-ignored distractor locations should be lower than that for the neutral locations (a probe suppression effect). However, we found no such probe suppression effect. It was absent both when the cued-to-be-ignored distractor locations changed randomly from trial-by-trial (Experiment 1) and when they were fixed (Experiments 2-4). It was absent even when the cued-to-be-ignored locations contained a salient color singleton to further incentivize suppression at those locations (Experiment 3) and when only a single distractor location was cued (Experiment 4). We propose that people accomplish selectivity either by blanketing suppression across all irrelevant locations (e.g., both threatening and non-threatening distractor locations), or by mainly boosting target locations.