Salting the water causes the proteins in both the thin, and thick albumin to coagulate. This makes them separate from the Inner shell membrane, making them easier to peel so they look nice, with no chunks missing. On a hard-boiled egg, it doesn't make that much difference, but it is really noticeable on a soft-boiled egg, as they are much more delicate. On medium. to hard-boiled eggs, here is a restaurant trick to make your eggs peel clean and intact. When the eggs are boiled, place the whole pot under running cold water in the sink and leave them for 5 minutes or so. Instead of cracking the shell by banging it on the counter, lay the egg on the counter, apply gentle, even pressure, and roll it around on the table, allowing the shell to crack as it goes. Roll each surface of the egg on the counter. Now, all you have to do is start a small piece of the shell, and the whole thing will come off in one piece, more or less, leaving a nice, clean, intact egg.