The role of morphological and syntactic information in non-native second language (L2) comprehension is controversial. Some have argued that late bilinguals rapidly integrate grammatical cues with other information sources during reading or listening in the same way as native speakers. Others claim that structural cues are underused in L2 processing. We examined different kinds of modifiers inside compounds (e.g. singulars vs. plurals, *rat eater vs. rats eater) with respect to this controversy, which are subject to both structural and non-structural constraints. Two offline and two online (eye-movement) experiments were performed examining the role of these constraints in spoken language comprehension of English and German, testing 77 advanced L2 learners. We also compared the L2 groups to corresponding groups of native speakers. Our results suggest that despite native-like sensitivity to the compounding constraints, late bilinguals rely more on non-structural constraints and are less able to revise their initial interpretations than L1 comprehenders.