This paper formalizes the optimal design of randomized controlled trials (RCTs) in the presence of interference between units, where an individual's outcome depends on the behavior and outcomes of others in her group. We focus on randomized saturation (RS) designs, which are two-stage RCTs that first randomize the treatment saturation of a group, then randomize individual treatment assignment. Our main contributions are to map the potential outcomes framework with partial interference to a regression model with clustered errors, calculate the statistical power of different RS designs, and derive analytical insights for how to optimally design an RS experiment. We show that the power to detect average treatment effects declines precisely with the ability to identify novel treatment and spillover estimands, such as how effects vary with the intensity of treatment. We provide software that assists researchers in designing RS experiments.