I'm reviving this thread because there is a lot information here that has not worked for me.
1. Vinegar. It seems to coagulate the white nicely but the texture and mouthfeel is abominable.
2. The swirling vortex. It slows to a crawl after the first egg is in.
3. Sous vide. As far as I'm concerned, the cooking temperature is in the danger zone far too long.
4. Fresh eggs. Yes this helps but no one says how to get them.
5. Deep pot only/shallow pan only: Both work wonders if you are careful.
Here is what I do, with minimal failure:
1. I use very fresh, even day old farm gate eggs, from pastured hens. Once in awhile I go to a source with indoor hens, and regular Purina feed. I won't pay extra for organic eggs, because the hens still eat Purina, although organic. Would you trust Purina for organic feed?
2.If I was in the city, I'd get farmers market eggs and ask a lot of questions. How can you ask questions about supermarket eggs?
3. I use a 6" pot for 2-3 eggs with 4" water. If I have to do a dozen or more I use a chicken fryer pan, with just enough water to cover the eggs.
4.I bring the water to a slow simmer, crack in the eggs, and cover for 4 minutes.
5. Remove with a slotted spoon or fish lifter. On a SS or CI pan there may be very slight sticking, because the burner was on for duration of cooking. So I am careful, and removing is easy.
Above is a sample photo. One dominant feature is the raised yolk, sitting firmly above the albumen. Only fresh eggs are like this.