It has been suggested that second languages and translated languages are constrained by aninterplay of several linguistic systems. This paper reports on a data-driven quantitativestudy on constrained Finnish. We detect linguistic phenomena that distinguish constrained from non-constrained Finnish across constrained varieties, first/source languages, and registers. Implementing a two-phase method, we first detect key quantitative differences of syntactically defined POS bigrams between each variety-, language-pair- and register-specific constrained dataset and its non-constrained counterpart, using Boruta feature selection. We then use the results as variables in a Multi-dimensional Analysis. The results show that both nominal complexity and verbal/clausal complexity distinguish constrained from non-constrained Finnish. These differences interact with both type of constraint and register: the constrained varieties are less sensitive to register differences, and this tendency is more pronounced in learner Finnish than in translated Finnish. Leaving out any of these variables from the analysis would blur our view of this multi-faceted phenomenon.