The worst thing you can do to a soon-to-be-boiled egg is to start it in cold water. If you bring your eggs cold to boiling hot with the water from the refrigerator, the membranes will fuse with the whites, resulting in damaged, scarred, devilish eggs. (And no, I’ve never found the vinegar trick helpful.)
I like to start my (pierced) eggs in boiling water, let them boil for 10 minutes, then dip them in an ice bath (if there is a whole bunch) or rinse them under cold water (if there are few and I plan.) eat immediately). I rarely have problems with peeling. I would say that I come across an egg that is easily indelible about every dozen, which is permissible considering that eggs and their shells are made up of complex organic systems.
You can also steam your eggs with similar effects (and very delicate whites). Just fill a saucepan with about an inch or an inch of water, put a steamer basket in it, cover it and bring it to a boil over high heat. Add the eggs and cook for 11-12 minutes before cooling in an ice bath or under cold running water.
