We investigated the role of cue weighting, second language (L2) proficiency, and L2 daily exposure in L2 learning of suprasegmentals different from the first language (L1), using eye-tracking. Spanish monolinguals, English-Spanish learners, and Mandarin--Spanish learners saw a paroxytone and an oxytone verb (e.g., "FIRma-firMÓ" "s/he signs-signed"), listened to a sentence containing one of the verbs, and chose the one that they heard. The three languages have contrastive lexical stress, but suprasegmentals have a greater functional load in Mandarin than in English. Monolinguals predicted suffixes accurately with both stress conditions and favored oxytones, but learners predicted suffixes accurately only with oxytones, the condition activating fewer lexical competitors. Monolinguals predicted suffixes accurately sooner but at a slower rate than did learners. L2 proficiency, but not L1 or L2 exposure, facilitated L2 predictions. In conclusion, learners of a contrastive-stress L1 rely on L2 suprasegmentals to the same extent as monolinguals, regardless of their L1. Lower L2 proficiency and higher cognitive load (more lexical competitors) reduce learners' reliance on suprasegmentals.