Via two reading experiments, this exploratory study examined the effects of over- and under-specified linguistic input on L2 online processing of Chinese referring expressions (REs). In each experiment, a group of advanced L2 Chinese speakers (all with Uyghurs as L1) and a control group of native Chinese speakers read 48 sets of 4 sentence pairs with each set including one sentence pair containing referential underspecification (ambiguity) and one pair containing overspecification (redundancy). An analysis of the two groups' reaction time (RT) using mixed-effects linear modelling reveals that underspecification had no effect on native Chinese speakers in both experiments, and overspecification also had no effect in the form of a redundant size noun modifier in Experiment 1 but showed a facilitating effect in the form of a color noun modifier in Experiment 2. In contrast, L2 Chinese speakers were significantly disrupted by underspecification in both experiments but not by overspecification. The results seem to support the hypothesis that L2 processing is constraint-based. Tentative research and pedagogical implications of the findings are discussed.