This chapter explores the common ground shared by non-native (L2) and translated language (TrL), seen as instances of constrained language use. It has been suggested that these diverge from native non-translated language (L1) in consistent ways. We explore this hypothesis in a corpus-driven manner, comparing written English in its L2 and TrL varieties, setting them against the benchmark of the L1 variety. In an attempt to control for confounding variables, we include two first/source languages for the constrained varieties, as well as three registers (argumentative writing, political speeches and tourism-related communication), which also allows us to increase representativeness. Methodologically, we look at frequencies of part-of-speech dependency bigrams, adopting keyness analysis and multidimensional analysis to detect and interpret differences between the contrasted varieties. The strengths of the approach are that it relies on syntactically parsed data instead of shallow part-of-speech sequences, is fully data-driven and can be easily implemented in different languages. Results indicate a tendency for the constrained varieties to rely on post-nominal modification and common nouns with determiners to a greater extent than non-constrained varieties, and to display a peculiar use of syntactic structures including proper nouns. Registers are found to impact greatly on results, and cross-register differences to be less prominent in the constrained varieties, which might point to a less heightened sensitivity to register conventions when performing language tasks under constraint of another language. Given the vast amount of variation in the data, the contribution ends on a note of caution when generalizing over-interpretations of constrained language data.