Q. Is there anything you can do to make hard-cooked eggs easier to peel?
A. It sounds like you started with very fresh eggs. The fresher eggs are, the harder they are to peel. Eggs from the supermarket usually are a least a week old, so they're not as much of a problem. But very fresh eggs, such as eggs from a farmers market, can be the devil to peel without tearing up the whites.
If you've cooked a lot of eggs for deviled eggs and find the batch is hard to peel, there are a couple of things you can try. First, make sure the eggs are completely cool before starting. Crack each one, then let them sit covered with cold water. Letting a little water get between the shell and the membrane will help separate the shell.
Before peeling, gently roll the egg around on a hard surface to crack it all over. Try to nick a little piece of membrane when you start pulling away the shell, which will also help to get the shell started.
If little pieces of shell are still stuck to the egg, swish it under cold water to get them off.