Three performance models with different complexity are used in numerical optimizations to construct powercurves of a flexible-kite, pumping airborne wind energy system. The mean cycle power is optimized over theoperation variables for a range of wind speeds. The optimal power curves following from the different modelsare compared. The model with the highest complexity allows optimizing over a set of operation settinsthat characterizes the overall shape of the pumping cycle trajectory. The optimal trajectory shape is highly dependent on the wind speed and shear.