Three minutes is for soft boiled, Mr. Ed.
For hard-cooked; I put mine in regular unsalted tap water, bring to a boil, and let 'em go for ten minutes after that. Then remove from heat, drain, and replace water with cold from the tap. Peel when cool. I seem to get the best results for easy peeling that way. Here's a tip; Hard boiled is one place you do NOT want just-laid eggs. They're nearly impossible to peel when that "young".
And now for a bit of fun:
If you'd like to Amaze Your Friends and Confound Your Enemies, now's a perfect time to learn to
blow a whole egg out of its shell using only your two lips.
Click here for educational video! :B