Ok, I'll try to explain what works for me. Same as most of the posts already, I cover the eggs with water, bring to a boil, cover with a lid and turn heat off....leave on the burner though, for 20 minutes. Then plunge in cold water. Here's the tricky part - I lightly crack each end of the egg on the countertop, then tap & roll GENTLY to crack the rest of the eggshell. Pick up the egg and gently turn/roll using a little pressure with fingertips, keep turning until you feel the shell & membrane release from the egg. Most of the time the whole shell comes right off in one piece held together only by the membrane. Is that clear as mud? Good luck.