The density, regularity, and efficiency of the coils wound on a stator (e.g., an electric motor stator) are improved by providing winding needle trajectories which tend to urge the wire to fill empty areas which may otherwise develop in the coils at the ends of the stator. The phase relationship between the oscillation and reciprocation components of needle motion is selected to optimize coil formation. In particular, each oscillation stroke is typically somewhat delayed (as compared to the prior apparatus) relative to the reversal of reciprocation direction. The reciprocation stroke length is also typically increased. Needle actuation apparatus in which adjustment of these parameters is facilitated is also disclosed.