Learning Cantonese tones is challenging for Mandarin speakers. Various factors are reported to affect non-native tone perception, and they include both linguistic ones such as L1 status, pitch correlates and extra-linguistic ones like presentation order. Whether and how these factors function and interact in non-native tone learning are yet well understood. Cantonese rising (high-rising T25, low-rising T23) and level (mid-level T33, low-level T22) tone contrasts share similar contours but differ in pitch heights. The phonetic (dis)similarities turn these tone pairs most difficult for Mandarin listeners. This study focusing on these two contrasts designed a short-term auditory training to help Mandarin listeners improve their perceptual discrimination of Cantonese tones. The training used tone pairs in different within-pair presentation orders: low-high (T23-T25, T22-T33) or high-low (T25-T23, T33-T22). Tone type (rising vs level) and segment familiarity (familiar vs unfamiliar) were independent variables. Results indicated significant improvement in tone discrimination by Mandarin participants who were exposed to input presented in low-high order and that improvement among the rising tone pairs was notably greater. The beneficial effect of low-high presentation order suggested effectiveness of more discernible input in acquisition of non-native phonological contrasts.