Egg shells

I've been annoyed lately whenever I try to make egg salad. Those dang shells stick to the egg whites more tightly than a balding man to the last remaining hairs of his comb-over. I've asked Google, and she referred me to several web sites that have varying opinions.
A common idea was that fresh eggs always stick (I can attest to that from back when I had some hens). However, these recent boiled eggs certainly are not all that fresh. I'm thinking the eggs I've been getting are some new breed of chicken or from chickens given feed that makes their egg shells stick no matter the age of the egg.
Another site said that fresh eggs have a pH around 7.9 when fresh, and over time, the pH increases to around 9, and something about that causing carbon dioxide to exit the egg, and the membrane becomes thinner and sticks less. Others said to lightly crack the eggs after boiling, and then put in cold water to cool, and then peel.
Other sites said a trick is to put a tablespoon of vinegar into the water. This one seemed to contradict the pH explanation, since vinegar has a pH of somewhere between 2.4-3.4 -- if I wanted to raise the pH, it would seem I should be adding baking soda, which has a pH of around 8.2.
So, being the stats nerd that I am, I decided to try an experiment, albeit not really all that scientific -- I didn't want to mess with more than 2 pots and 4 eggs. So we'll say the control group was the eggs I boiled last night, and the experimental eggs I boiled tonight had a terribly low sample size. Anyway, to one pot went 1 tablespoon of vinegar and two eggs, to the other, 1 tablespoon of baking soda. I brought both to a boil, and set the timer for 10 minutes. Afterward, I removed the eggs, labeled them, and made a small crack at the top of the shell on the large end of one egg from each pot. They immediately went into a bowl of ice water for 20 minutes, and then were peeled.
The results:

Cooking Method	Peeling result
Baking soda, cracked shell	Peeled cleanly, but shell was a little difficult to remove.
Baking soda, uncracked shell	Lost lots of white due to heavy sticking.
Vinegar, cracked shell	Peeled fairly easily and cleanly.
Vinegar, uncracked shell	Peeled cleanly, fairly easy shell removal.

So there you have it. Add a tablespoon of vinegar to the water, and then lightly crack the shells before cooling in cold water.
And before you say I'm such a geek, remember that you'll most likely be trying this technique too!