Ionin, Ko and Wexler (2004a) have shown that L2 speakers of English whose L1’s lack articles (Russian and Korean) appear to fluctuate in their interpretation of the and a, allowing them to encode either definiteness or specificity. They argue that these are two options of an Article Choice Parameter offered by Universal Grammar, and that the Russian and Korean speakers fluctuate between them when they are acquiring English. In the present study it is shown that a similar pattern can be observed in L2 speakers of English whose L1 is Japanese (also a language that lacks articles) but not in speakers whose L1 is Greek, a language with articles that encode definiteness like English. It is also shown that while group results for the Japanese speakers suggest fluctuation, individual results do not. It is argued that an account can be given of both cases which does not require appeal either to an Article Choice Parameter or to the concept of ‘fluctuation’. The alternative proposal made here is consistent with Universal Grammar, and follows from an organisation of the grammar where phonological exponents are separated from the lexical items manipulated by syntactic computations, as in Distributed Morphology. It is suggested that a descriptively adequate account which avoids a construction-specific parameter like the Article Choice Parameter and departure from the normal assumptions of UG represented by fluctuation should be preferred.