Speech is more difficult to understand when it is presented concurrently with a distractor speech stream. One source of this difficulty is that competing speech can act as an attentional lure, requiring listeners to exert attentional control to ensure that attention does not drift away from the target. Stronger attentional control may enable listeners to more successfully ignore distracting speech, and so individual differences in selective attention may be one factor driving the ability to perceive speech in complex environments. However, the lack of a paradigm for measuring nonverbal sustained selective attention to sound has made this hypothesis difficult to test. Here we find that individuals who are better able to attend to a stream of tones and respond to occasional repeated sequences while ignoring a distractor tone stream are also better able to perceive speech masked by a single distractor talker. We also find that participants who have undergone more musical training show better performance on both verbal and nonverbal selective attention tasks, and this musician advantage is greater in older participants. This suggests that one source of a potential musician advantage for speech perception in complex environments may be experience or skill in directing and maintaining attention to a single auditory object.