Ah, the wonders of getting eggs peeled, finally explained, from the guide to eggs at www.georgiaeggs.org, where you'll find everything you ever did, or did not, want to know about that wonderful subject:
PEELING Removing the shell and membranes from a hard-cooked egg.
Opinion among researchers is divided as to whether or not salt in the cooking water helps make hardcooked eggs easier to peel. Some research indicates that a 1 to 10% salt level (2 to 4 tablespoons per gallon of water) makes unoiled eggs easier to peel, but peelability of oiled eggs is not significantly affected. Almost all eggs available on the consumer market are oiled while commercial purchasers may specify unoiled eggs. Most researchers agree that using eggs that are "not too fresh" will help make peeling easier.
A nicely centered yolk makes very attractive deviled eggs and garnishes. However, as an egg ages, the white thins out which gives the yolk more opportunity to move about freely. This can result in a displaced yolk when the egg is hard-cooked. Using the freshest eggs possible will minimize this displacement, but very fresh eggs are more difficult to peel after hard-cooking. The air cell that forms between the shell membranes as the egg ages helps to separate shell from egg, but in very fresh eggs the air cell is still small. The best compromise for attractive eggs with centered yolks that are relatively easy to peel seems to be using eggs that have been refrigerated for about a week to 10 days. Some new research suggests that yolk centering may be better if eggs are stored small-end up for 24 hours before hard-cooking.
Piercing the shell before cooking may also make peeling easier.
Thoroughly cool the egg immediately after cooking in a bowl of ice or under running cold water (5 minutes isn't too long). Peel right after cooling for immediate use or refrigerate in the shell in the carton for use within 1 week. Crackle the shell all over by tapping gently on a table or counter top. Roll the egg between the hands to loosen the shell. Then peel it off, starting at the large end. Hold the egg under running water or dip it in water to make peeling easier.