The following directions are a little fussy, but well worth it as it produces perfect eggs every time. Put raw eggs into a pot large enough to hold them comfortable and cover with enough cold water to stand at least one inch above them.  Over a high heat, bring to a boil and continue to boil for 5 minutes.  Remove from the heat, cover with a tight fitting lid and allow to sit for 20 minutes.  Remove from the pot and place in a bowl of cold or even ice water to chill the eggs as soon as possible.   Crack the shells and return the eggs to the cold water and allow them to sit for about an hour.  This allows water to seep under the shell through the cracks and helps to loosen the shells. A truly fresh egg, however, will defy all efforts to peel nicely.  As an egg sits gas developers between the egg and the shell and the more of this gas there is the easier it is to peel the egg.  Given this, you can see that when you buy eggs at the store and they peel easily, they are not truly fresh eggs.  If they were you could not peel them with any ease at all.  Almost all the eggs you buy at the grocery store are two to three weeks old.  There is nothing wrong with that.  Eggs have quite a long shelf life if handled correctly. Something else that may help boiled eggs to peel easily is to use a push-pin and make a small hole in the large end of each egg before boiling them.  However, nothing, absolutely nothing will help if you have a truly fresh egg laid by a determined hen.