(I do sleep on my side, but this idea has never occurred to me, and I tend to picture other people lying tidily on their backs - so I was picturing someone sleeping on their back with a pillow placed in an unaccountable position.)
Will be trying this tonight.
I picked up the practice originally after long hikes. It's amazing how much it helps with the soreness.
I just take a regular, commodity pillow and fold it in half. Any kind you can get at your local store works great!
Can you share any details about that "regular pillow?" Ideally an online link that will ship internationally, but failing that: Materials, thickness, density, really anything that might be relevant would be helpful.
I also find lower leg straight and upper leg on the pillow (so you look like an 'h') works really well.