Policymakers advocating for later school starting times argue that increased sleep duration may generate important schooling benefits. Using data from the National Longitudinal Study of Adolescent Health, this study examines the relationship between sleep duration and academic performance, while carefully controlling for difficult-to-measure characteristics at the family- and individual-levels. We find that increased sleep time is associated with improvements in classroom concentration as well as increased educational attainment. However, we also find evidence of diminishing returns to increased sleep. We estimate an "academic optimum" number of sleep hours of, on average, 8.5 hours per night. Turning to sleep quality, we find that the onset of insomnia-like symptoms is associated with diminished contemporaneous academic concentration, but little change in longer-run educational attainment.