It is the temperature of the water that cooks the eggs. A good simmer as to a hard rolling boil is the same temperature. So if you remove the eggs from the source of heat at the height of a good simmer and follow through with the rest of your procedure (however you do it) you will always avoid that hated green ring around the yolk. If you choose to use the pin on the large end of the egg, be careful you don't pierce the white lining that protects the egg. Then your whites will stay inside where they belong.
Illegitimi non carborundum!
I don't want my last words to be, "I wish I had spent more time doing housework"