The current understanding of how birds fly must be revised, because birds use their hand-wings in an unconventional way to generate lift and drag. Physical models of a common swift wing in gliding posture with a 60 degrees sweep of the sharp hand-wing leading edge were tested in a water tunnel. Interactions with the flow were measured quantitatively with digital particle image velocimetry at Reynolds numbers realistic for the gliding flight of a swift between 3750 and 37,500. The results show that gliding swifts can generate stable leading-edge vortices at small (5 degrees to 10 degrees) angles of attack. We suggest that the flow around the arm-wings of most birds can remain conventionally attached, whereas the swept-back hand-wings generate lift with leading-edge vortices.