To investigate large library docking’s ability to find molecules with joint activity against on-targets and selectivity versus antitargets, the dopamine D₂ and serotonin 5-HT_2A receptors were targeted, seeking selectivity against the histamine H₁ receptor. In a second campaign, κ-opioid receptor ligands were sought with selectivity versus the μ-opioid receptor. While hit rates ranged from 40% to 63% against the on-targets, they were just as good against the antitargets, even though the molecules were selected for their putative lack of binding to the off-targets. Affinities, too, were often as good or better for the off-targets. Even though it was occasionally possible to find selective molecules, such as a mid-nanomolar D₂/5-HT_2A ligand with 21-fold selectivity versus the H₁ receptor, this was the exception. Whereas false-negatives are tolerable in docking screens against on-targets, they are intolerable against antitargets; addressing this problem may demand new strategies in the field.