Previous research has shown a learning effect on speech perception in nonstationary maskers. The present study addressed the time-course of this learning effect and the role of informational masking. To that end, speech reception thresholds (SRTs) were measured for speech in either a stationary noise masker, an interrupted noise masker, or a single-talker masker. The utterance of the single talker was either time-forward (intelligible) or time-reversed (unintelligible), and the sample of the utterance was either frozen (same utterance at each presentation) or random (different utterance at each presentation but from the same speaker). Simultaneously, the pupil dilation response was measured to assess differences in the listening effort between conditions and to track changes in the listening effort over time within each condition. The results showed a learning effect for all conditions but the stationary noise condition - that is, improvement in SRT over time while maintaining equal pupil responses. There were no significant differences in pupil responses between conditions despite large differences in the SRT. Time reversal of the frozen speech affected neither the SRT nor pupil responses.