With the increasing focus of genetic association on the identification of trait-associated rare variants through sequencing, it is important to identify the most cost-effective sequencing strategies for these studies. Deep sequencing will accurately detect and genotype the most rare variants per individual, but may limit sample size. Low pass sequencing will miss some variants in each individual but has been shown to provide a cost-effective alternative for studies of common variants. Here, we investigate the impact of sequencing depth on studies of rare variants, focusing on singletons-the variants that are sampled in a single individual and are hardest to detect at low sequencing depths. We first estimate the sensitivity to detect singleton variants in both simulated data and in down-sampled deep genome and exome sequence data. We then explore the power of association studies comparing burden of singleton variants in cases and controls under a variety of conditions. We show that the power to detect singletons increases with coverage, typically plateauing for coverage > ~25x. Next, we show that, when total sequencing capacity is fixed, the power of association studies focused on singletons is typically maximized for coverage of 15-20x, independent of relative risk, disease prevalence, singleton burden, and case-control ratio. Our results suggest sequencing depth of 15-20x as an appropriate compromise of singleton detection power and sample size for studies of rare variants in complex disease.