Aerodynamic theory predicts that the power required for an animal to fly over a range of speeds is represented by a ‘U’-shaped curve, with the greatest power required at the slowest and fastest speeds, and minimum power at an intermediate speed. Tests of these predictions, based on oxygen consumption measurements of metabolic power in birds and insects, support a different interpretation, generating either flat or ‘J’-shaped power profiles, implying little additional demand between hovering and intermediate flight speeds. However, respirometric techniques represent only an indirect assessment of the mechanical power requirements of flight and no previous avian study has investigated an animal’s full range of attainable level flight speeds. Here we present data from in vivo bone-strain measurements of pectoralis muscle force coupled with wing kinematics in black-billed magpies (Pica pica), which we use to calculate mechanical power directly. As these birds flew over their full range of speeds, we offer a complete profile of mechanical power output during level flapping flight for this species. Values of mechanical power output are statistically indistinguishable (that is, the power curve is flat) over most forward-flight speeds but are significantly higher during hovering and flight at very low speeds.