Dual-task interference often arises when people respond to an incoming stimulus according to an arbitrary rule, such as choosing between the gas pedal and the brake when driving. Severe interference from response selection yields a brief "Psychological Refractory Period," during which a concurrent task is put on hold. Here, we show that response selection in one task does not always hamper the processing of a secondary task. Responding to a target may paradoxically enhance the processing of secondary tasks, even when the target requires complex response selection. In three experiments, participants encoded pictures of common objects to memory while simultaneously monitoring a rapid serial visual presentation (RSVP) of characters or colours. Some of the RSVP stimuli were targets, requiring participants to press one of the two buttons to report their identity; others were distractors that participants ignored. Despite the increased response selection demands on target trials, pictures encoded with the RSVP targets were better remembered than those encoded with the RSVP distractors. Contrary to previous reports and predictions from dual-task interference, the attentional boost from target detection overcomes increased interference from response selection.