I was taught to introduce the side reins via a sliding inside rein only at first... Lungeline goes through the bit ring to the lowest ring possible, as low as the point of elbow... But generally point of shoulder is low enough for a horse with an already lower center of balance.
The concept was to teach the horse to flex to the inside and give to the bit before you add the "rigid" outside rein. You go as low as possible to encourage the horse to drop the head and raise it's back, and gradually raise the height of the line as the horse's fitness and balance improves. (which simulates what I was taught as correct training... Start low and come higher as ability dictates, using the inside rein to ask for flexion/bend and the outside rein to encourage straightness).
The outside rein is added when the horse has learned to give softly to the bit and is ready to learn to carry itself straight and round. It was said to be more likely to cause cnfusion and evasion issues if added before that point. I was shown to adjust it so that there was slack until the horse's head came just slightly ahead of the verticle when the poll was level with the wither.
I was actually taught that two fixed side reins can be counter productive as a clever horse can learn to brace on the bit rather than stay soft. (it takes more skill from the handler to know when to correct the horse in two fixed reins). One of my coaches never uses the outside rein at all, she said when she was learning from a German master he explained it was unnecessary and can make it harder to see when the horse is truly using itself well (I am paraphrasing a bit... The explanation was pretty in depth)
Not saying either way is actually more correct, I just find it interesting the different approaches.
In Pony Club I was taught the method described in above posts... But figured I must still have it wrong because they never seemed to work well for me and generally I would simply opt not to use them because they never seemed to do more good than not.
The method I outlined in my post helped my horses, immensely, and directly reflected into the saddl, far more so than the PC method... So either I really had been doing something wrong originally, or, for me and the training issues I was encountering anyhow, the method I was shown by my two latest coaches just works better for me.