Judicial independence (JI) is a concept commanding an expansive literature. However, the findings in the literature are inconsistent: Measures of de facto and de jure JI have been shown to be uncorrelated, negatively correlated, or weakly positively correlated with each other. I argue that the inconsistent findings are the result of conceptual fuzziness and errors in measurement. As a corrective, I define JI as the conjunction of judicial discretion and judicial preferences. This definition leads to the identification of two separately necessary and jointly sufficient conditions for judicial independence: high discretion and preferences that diverge from the actors whose policy they can veto. I argue that when constitutions are difficult to amend, judiciaries have more discretion in their ability to interpret constitutional matters. However, because judicial preferences are generally unobservable, the relationship between JI and constitutional rigidity will be heteroskedastic. I operationalize JI as the proportion of a sitting government’s bills that the judiciary strikes down on constitutional grounds. The expected relationship – that both the mean and variance of JI are increasing in constitutional discretion – is corroborated.