Mandatory disclosure of evidence (the so-called Brady rule) is considered to be among the most important bulwarks against prosecutorial misconduct. While protecting the generality of defendants in the criminal process, we show that under certain reasonable assumptions, this procedural mechanism may hurt innocent defendants by inducing prosecutors to adjust their behavior to their detriment. The main rationale for our thesis is that, if forced to reveal exculpatory information, the prosecutor might not look for that information in the first place, and in turn this could harm the innocent under certain reasonable conditions. We extensively discuss our results in the context of the economic literature on criminal procedure.