This really isn't a recipe as much as a method. I never could get a decent egg to the table - it would crust on the bottom before it was done, or overcook or... Then I read about this method in an old "Heloise" book (for you younger ladies,there was a first Heloise in the 60's who was today's Heloise' mom!)
After just a little practice in timing, I have made perfect eggs - from soft to firm - every time!
Heat skillet to medium heat (never hot!). Put about one tablespoon of oil, bacon grease or butter in heated skillet, if large, for a small skillet use a little less.
Drop eggs into the pan, salt and pepper them,and add about 1/8 cup of water. Cover tightly and leave alone for a few minutes, On my stove it takes about 3 minutes for a soft cooked egg, and 4 minutes for firm. The eggs are cooked perfectly and are not greasy at all.
You will need to experiment to find out exact timing on your stove, you may also need to adjust the water or butter, but once you get it figured out I believe your eggs will come out perfect every time. I hope it works as well for you as it has for me!