lubricant addition on drawn wire for springcoiling

Hello everybody,
I have a stainless steel wire that is drawn to 3.6mm dia and ready for coiling at spring machine. However, we believe that the residual lubricant on surface from drawing soap is too little. This means high friction and tool wear and surface problems on coiled springs.
Can anyone suggest how to improve the lubrication on the drawn wire so that it can be coiled properly with low friction??
I cannot redraw the material so just looking for a lubricant coating that can be put on this drawn wire and coiled thereafter.
Thanks in advance.
Amandeep