Turn the heat down to just simmer, once you put the eggs into the boiling water. It's the boiling that makes the green-gray ring around the yolk, plus timing is crucial too. As Lorraine stated, immediately rinse under cold water as soon as time is up, or they will continue to cook inside the shell.

All is not lost though ... I love eggs, hate to waste even if there's the dark ring .... so, I make egg salad, and mix some dijon or horseradish in with the mayonnaise ... gives a peppery bite that "disguises" the overcooked-ness of the egg...

Doreen