We analyze admission and discharge decisions when hospitals become capacity constrained on high-demand days, and develop a test for discrimination that, under certain circumstances, does not require controls for differences across patient groups. On high-demand days, patients are discharged earlier than expected compared to those discharged on low-demand days. High demand creates no statistically significant differences in hospitals' admission behavior. Thus, hospitals appear to ration capacity by hastening discharges rather than by restricting admissions. We could not reject a null hypothesis of no discrimination against Medicaid patients in discharges.