How aerodynamic power required for animal flight varies with flight speed determines optimal speeds during foraging and migratory flight. Despite its relevance, aerodynamic power provide an elusive quantity to measure directly in animal flight. Here we determine the aerodynamic power from wake velocity fields, measured using tomographical particle image velocimetry, of pied flycatchers flying freely in a wind tunnel. We find a shallow U-shaped power curve, which is flatter than expected by theory. Based on how the birds vary body angle with speed, we speculate that the shallow curve result from increased body drag coefficient and body frontal area at lower flight speeds. Including modulation of body drag in the model results in a more reasonable fit with data than the traditional model. From the wake structure we also find a single starting vortex generated from the two wings during the downstroke across flight speeds (1-9 m/s). This is accomplished by the arm wings interacting at the beginning of the downstroke, generating a unified starting vortex above the body of the bird. We interpret this as a mechanism resulting in uniform downwash and low induced power, which can help explain the higher aerodynamic performance in birds compared to bats.