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Recent empirical analyses dispute the significance of constitutional rigidity, while the traditional position it is the most important part of a constitution. This article argues that the dispute is due to the misuse of independent and dependent variables, as well as inappropriate methodology. I use the theory of veto players to measure constitutional rigidity, and create a new index covering 94 democratic countries. First, I explain the underlying logic of the veto players approach and the specific derivation of the rules for the construction of the rigidity index. Second, I explain why the lack of constitutional rigidity is a necessary but not sufficient condition for significant constitutional amendments in democratic countries. Finally, I create a new dataset on the significance of constitutional amendments and estimate a heteroskedastic model, in which more significant amendments lead to a better fit. I also point out other areas where constitutional rigidity can be used.