Measuring the properties of the Higgs boson is one of the most important missions for Run 2 of the LHC. These measurements can be understood and optimised with intuitive and powerful tools from information geometry. The central object of this approach is the Fisher information matrix, which defines the maximum precision with which theory parameters can be measured in a given experiment. We calculate the information on effective dimension-six operators in different Higgs signatures. We demonstrate how these results let us improve event selections, determine the most powerful observables, and compare the power of modern multivariate techniques to that of traditional histogram-based analyses.