So after reading some of the discussion, I had to go it alone.
I've always been taught that the best thing is to put the eggs into cold water, bring the water to a boil, cover pot, remove from heat, wait 10 or 11 minutes and you have perfect eggs...and the yolk IS a lovely-never-gray-green color. But that was the method that I used two weeks ago. Not. Good.
So yesterday morning, I dropped a room temperature egg (so very unAmerican, to keep my eggs on the counter) into rapidly boiling water. Lowered the heat, cooked it 10 minutes and peeled it immediately under cold, running water so I could handle it. Perfect egg.
But the request had come out: try the other methods. So I put the eggs back into the fridge (because face it, most Americans DO keep their eggs in the fridge).
Egg 1: Cold egg into cold water. Poor results. As expected. (This is how I cooked them two weeks ago.)
Egg 2: Cold egg into cold water with about 1/2 teaspoon baking soda. Maybe marginally better, but still ugly and difficult to peel.
Eggs 4and 5: Cold eggs into rapidly boiling water: They didn't explode! And they peeled so easily! I left the shells on the plate so you could see how big the pieces I took off were.