Abstract: A spinning apparatus winds a strand onto a yarn package by relatively rotating a flyer and the yarn package about an upright axis so as to wind the strand in a succession of turns around the package by a flyer finger movable axially relative to the package. Each successive layer of turns is shorter than the preceding one so that the finished package has an axially upwardly tapered upper end. After substantially completely forming the package the rotation is generally stopped to leave the flyer in a position with the finger below the upper end of the last layer of turns formed on the package. Then the package and finger are relatively axially moved until the finger is generally at the upper end of the first layer of turns formed on the package. The flyer and package are then relatively rotated forward, that is in the same direction as when the package was being formed, through at least one half revolution about the axis so as to form a loop of the strand around the upper package end.