When listeners hear a target signal in the presence of competing sounds, they are quite good at extracting information at instances when the local signal-to-noise ratio of the target is most favorable. Previous research suggests that listeners can easily understand a periodically interrupted target when it is interleaved with noise. It is not clear if this ability extends to the case where an interrupted target is alternated with a speech masker rather than noise. This study examined speech intelligibility in the presence of noise or speech maskers, which were either continuous or interrupted at one of six rates between 4 and 128 Hz. Results indicated that with noise maskers, listeners performed significantly better with interrupted, rather than continuous maskers. With speech maskers, however, performance was better in continuous, rather than interrupted masker conditions. Presumably the listeners used continuity as a cue to distinguish the continuous masker from the interrupted target. Intelligibility in the interrupted masker condition was improved by introducing a pitch difference between the target and speech masker. These results highlight the role that target-masker differences in continuity and pitch play in the segregation of competing speech signals.