When conducting instrumental variable studies, practitioners may exclude units in data processing prior to estimation. This exclusion step is critical for the study design but is often neglected. Here we view this problem as a well-defined tradeoff between statistical power and external validity, which can be navigated with a data driven strategy. Our method estimates the probability of units being compliant and increases statistical power by excluding units with low compliance probability. This data-driven exclusion criterion can help navigate the tradeoff between power and external validity for many quasi-experimental settings.