Syntactic variation of idioms covers many operations, from passive to pronominalizations to omission of complements. In the recent years, several authors claimed such operations to be correlated to one another, giving substance to a notion of one-dimensional syntactic flexibility. In a framework that allows for formal description within a discrete model, for such purposes as symbolic parsing, we test this claim by computing how much 11 syntactic operations are pairwise correlated on 2129 entries of Gross' (1982) lexicon-grammar of French idioms. On these samples, syntactic flexibility appears as a mix of phenomena so weakly correlated that information about one of them doesn't predict if others are applicable.