A breakthrough for me at least. Somehow I understood the conventional wisdom in peeling hard boiled eggs was to start at the large end where the air pocket is, so that's how I always started peeling eggs and more often than not it was a struggle, no matter how old the egg was. That membrane that is between the shell and the egg white clings so stubbornly to the white that I often mangled the egg or spent way too much time trying for a perfect egg by trying to separate that membrane under water.
But for the last three batches of hard boiled eggs I've made I discovered that starting from the pointed end--the end opposite the air pocket--makes it much easier to peel. Just this afternoon I boiled some eggs from a carton I just bought - expiration date April 12 - and by cracking the shell with the back of a spoon and peeling under water, like I always do, but starting at the pointed end, I was able to easily get between the membrane and the egg while and pull off all the shells in a neat spiral. White stayed intact.
So next time you make hard boiled eggs, start peeling from the pointed end and you should have success, regardless of the freshness or age of the egg. I was so surprised to discover that the "conventional wisdom" I've been operating under for more years than I care to admit was wrong.