In this paper, we operationalize register differences at the intersection of formality and mode, and distinguish four broad register categories: spoken informal (conversations), spoken formal (parliamentary debates), written informal (blogs), and written formal (newspaper articles). We are specifically interested in the comparative probabilistic/variationist complexity of these registers – when speakers have grammatical choices, are the probabilistic grammars regulating these choices more or less complex in particular registers than in others? Based on multivariate modeling of richly annotated datasets covering three grammatical alternations in two languages (English and Dutch), we assess the complexity of probabilistic grammars by drawing on three criteria: (a) the number of constraints on variant choice, (b) the number of interactions between constraints, and (c) the relative importance of lexical conditioning. Analysis shows that contrary to theorizing in variationist sociolinguistics, probabilistic complexity differences between registers are not quantitatively simple: formal registers are consistently the most complex ones, while spoken registers are the least complex ones. The most complex register under study is written-formal quality newspaper writing. We submit that the complexity differentials we uncover are a function of acquisitional difficulty, of on-line processing limitations, and of normative pressures.