I'm NOT patient enough, and too picky, to appreciate the pock-marked typical outcome of egg peeling. I happened upon this method a while back, and it WORKS!
1. After hard-boiling the eggs (cover with water, bring to a boil & simmer - covered - for 15 minutes), cool the eggs enough to handle.
2. Tap them lightly, just enough to crack the shell, in one of two places. A) Crack the shell around the entire egg, in the center - you should have one "line" of cracks around the thickest part of the egg; B) Crack the shell at the tip of the egg.
3. Insert the tip of a spoon into the crack, so that the shape of the egg nestles into the bowl of the spoon.
4. Use the spoon to lift and remove the shell. Keep the tip of the spoon angled away from the egg, to avoid gauging the egg.
Voila! A sleek quickly peeled egg, begging to be included in all sorts of fabulous dishes. Dishes like this: Garbanzo Alinados con Alcaparras