We examined what causes L1-L2 differences in sensitivity to prominence cues in discourse processing. Participants listened to recorded stories in segment-by-segment fashion at their own pace. Each story established a pair of contrasting items, and one item from the pair was rementioned and manipulated to carry either a contrastive or presentational pitch accent. By directly comparing the current self-paced listening data to previously obtained experimenter-paced listening data, we tested whether reducing online-processing demands allows L2 learners to show a nativelike behavior, such that contrastive pitch accents facilitate later ruling out the salient alternative. However, reduced time pressure failed to lead even higher proficiency L1-Korean learners of English to reach a nativelike level, suggesting that L2 learners' nonnativelike processing and representation of the prominence cue in spoken discourse processing can be due to the inherent difficulty of fully learning a complex form-function mapping rather than to online-processing demands.