We model optimal traveler responses to delays in the case of discrete departure time choice. We use both real and simulated data to illustrate our results, showing that passengers almost entirely offset their schedule delay costs increase, even in very unreliable systems. Our results suggest that, if the distribution of delays is sufficiently narrow, travelers fully offset the scheduling costs caused by delays. If the distribution of delays is wider, the amount by which schedule delay costs are offset decreases. This implies that, all else equal, more welfare can be gained by preventing incidental long delays than by reducing the average delay. © 2014 INFORMS.