We developed a relief strategy for assigning second-shift anesthetists to late-running operating rooms. The strategy relies on a statistical method which analyzes historical case durations available from surgical services information systems to estimate the expected (mean) remaining hours in cases after they have begun. We tested our relief strategy by comparing the number of hours that first-shift anesthetists would work overtime if second-shift anesthetists were assigned using our strategy versus if the anesthesia coordinator knew in advance the exact amount of time remaining in each case. Our relief strategy resulted in 3.4% to 4.9% more overtime hours for first- shift anesthetists than the theoretical minimum, as would have been obtained had perfect retrospective knowledge been available. Few additional staff hours would have been saved by supplementing our relief strategy with other methods to monitor case durations (e.g., real-time patient tracking systems or dosed circuit cameras in operating rooms). Implications: A relief strategy that relies only on analyzing historical case durations from an operating room information system to predict the time remaining in cases performs well at minimizing anesthetist staffing costs.