Hard boiled eggs

Folks, we got burned recently when we went to hard boil some eggs.  We made pork over rice and the shells stuck, badly.  We had non fresh eggs and followed all the rules.  I said swear words and threw them all in the trash.

I tried again using a different method and were rewarded, twice now, with shells that didn't stick.

Bring water to a boil in a small saucepan
Lower an egg into the water using tongs so it doesn't crack
Simmer for 13 minutes and then shock in ice water