The effect that varying power, while holding mean power constant, would have on cycling performance in hilly or windy conditions was analyzed. Performance for a 70-kg cyclist on a 10-km time trial with alternating 1-km segments of uphill and downhill was modeled, with mean (V) over dot O-2 (3, 4, 5 L.min(-1)), variation in (V) over dot O-2 (5, 10, 15%), and grade (0, 5, 10, 15%) used as independent variables. For the conditions of 4 L.min(-1), 10% variation, and 10% grade, results were as follows: finishing time of 22:47.2 with varied power, versus 24:20.3 at constant power, for a time savings of 1 min 33.1 s. Separately, a 40-km time trial with alternating 5-km segments of headwind and tailwind (0, 8, 16, 24 km h(-1)) was modeled, with the following results for the conditions of 4 L.min(-1), 10% variation, and wind speed of 16 km.h(-1): finishing time of 60:21.2 with power variation vs 60:50.2 at constant power, for a time savings of 29 s. Time saved was directly proportional to variation in (V) over dot O-2, grade, and wind speed and was indirectly proportional to mean (V) over dot O-2. In conclusion, the model predicts that significant time savings could be realized on hilly and windy courses by slightly increasing power on uphill or headwind segments while compensating with reduced power on downhill or tailwind segments.