Although many researchers have shown that listeners are able to selectively attend to a target speech signal when a masking talker is present in the same ear as the target speech or when a masking talker is present in a different ear than the target speech, little is known about selective auditory attention in tasks with a target talker in one ear and independent masking talkers in both ears at the same time. In this series of experiments, listeners were asked to respond to a target speech signal spoken by one of two competing talkers in their right (target) ear while ignoring a simultaneous masking sound in their left (unattended) ear. When the masking sound in the unattended ear was noise, listeners were able to segregate the competing talkers in the target ear nearly as well as they could with no sound in the unattended ear. When the masking sound in the unattended ear was speech, however, speech segregation in the target ear was substantially worse than with no sound in the unattended ear. When the masking sound in the unattended ear was time-reversed speech, speech segregation was degraded only when the target speech was presented at a lower level than the masking speech in the target ear. These results show that within-ear and across-ear speech segregation are closely related processes that cannot be performed simultaneously when the interfering sound in the unattended ear is qualitatively similar to speech.