My daughter did some eggs this morning...they were fresh and peeled fairly well. I was really surprised.
She put them in cold out of the tap water...they were already room temperature. They were only a day old so they had never gone into the frig yet.
She put salt in the water.
She brought them to a boil VERY slowly.
When they came to a boil she boiled them at a very slow boil for 5 minutes.
Then turned the fire off and let them sit in the pan for 10 minutes.
Then drain, since with tap water, drain just cover with water and add ice to the water.
Let them sit in the ice water about 5 minutes and then peel very gently.
I was very surprised they peeled at all.