"I think that I will continue to to say to myself Step Swing. Sway on three."

CBM, step, swing, sway (&CBM, step, ...)

Looking at the Hiltons natural turn ,there is a curve of the top part of the body to the right from stretching the sides in that direction which has nothing to do with sway ,but is in addition to sway and for effect,so just to step ,swing and sway won't make you look like a pro. We move faster into a natural turn of the quickstep with less sway than in the waltz so speed is not the only reason for sway?

Dave.To add to this. I find that men can manage to get CBM or CBMP when going foreward, But fail badly when going backwards. It is just as imortant there as it is going foreward. Unfortunately it is possible to dance with no CBM, like a block of wood but never the less dance. This is my method to train the muscles. Whatever I do going foreward I will imediatly do backwards. Say first step of the Feather Step with CBM. Turn around and make sure that I have the neccesary CBM after I am facing the other way. I got this idea from some Latin Classes I go to. We even had to do a Basic Rumba with step one beat two on the right foot and keep going.

I must change my early statement that ther is an aditional curving of the body at the end of sway. Having looked more carefully at the vidios I see that the sway starts very early on the first step(right foot) by staying low (not rising to soon) and make sure that the left foot extends to it's full length the top part of the body is left behind giving the sway,most of the sway is completed befor the weight moves on to the left foot. (The lady can help with the sway by stepping under her body with the left foot,this is my idea and may be bad advice for the lady.)