Recent proposals argue that interface areas such as syntax/semantics and syntax/pragmatics are particularly difficult for adult learners, in comparison to purely syntactic phenomena (Sorace 2003, 2004). In contrast, other research shows that L2 learners are able to acquire target representations even when the interpretation is not readily available in the input (Borgonovo, Bruhn de Garavito and Prévost 2005, Dekydtspotter and Sprouse 2001). In this paper we add to the growing literature on the acquisition of interpretational properties by showing that adult L2 learners can acquire knowledge of the syntactic correlates of the semantic notion of specificity in constructions involving topicalisation and null objects in Spanish. The learners’ first language (L1) is Brazilian Portuguese, where specificity does not play the role in these constructions that it plays in Spanish. Results show that learners can go beyond their L1 with respect to the acquisition of interface phenomena, suggesting that native-like grammars are attainable in L2 acquisition.