A single-twist wire stranding or bunching machine having a reciprocating flyer traversing the length of a take-up reel and rotating coaxially with respect thereto, such take-up reel being mounted within pivoting means to facilitate easy removal of the reel after it is fully wound with wire. The invented machine comprises electro-mechanical means for automatically controlling the uniformity of the lay length of the twisted wire by correcting for changes in the velocity of the wire being fed into the machine due to wire build-up on the reel or to reversals of the traversing flyer. Additional control means are also disclosed for automatically controlling the points at which the flyer, in its reciprocating motion, reverses direction, thereby minimizing wire accumulations or recesses at the end flanges of the reel.