Recent studies showed that having more preparation time during the cue-stimulus interval (CSI) can reduce the performance cost of switching attention between simultaneous voices – the so-called attention “switch cost”. Having established a benefit of preparation on the switch cost, we investigated how the CSI is used for preparing to direct attention on trials where the target speaker or location switches. There are two potential processes that could benefit from longer preparation: disengaging attention from the previously relevant voice and engaging attention to the newly relevant voice. To distinguish which of these processes underlies the reduction in attention switch cost with preparation, we used a cued attention switching paradigm in two experiments where, on each trial, voices would come simultaneously from two of three possible speakers (Experiment 1) or two of three possible locations (Experiment 2). By cuing either the identity/location of the target voice (in repeat and switch-to conditions) or a switch away from the previous target identity/location (in the switch-away condition), we could distinguish between disengagement of attention from the previous voice and engagement of attention to the new voice. In both experiments, we found that increased preparation time with switch-away cues reduced switch costs (relative to the repetition cue condition). Somewhat surprisingly, this effect was weaker in the switch-to condition (but these switch costs are not directly comparable due to the difference in working memory demand between these conditions). These data suggest that attentional disengagement is sufficient to produce a preparatory reduction of auditory attention switch cost.