soft-boiled eggs

I don't have a clear memory of how I was thought to cook soft-boiled eggs, which is sad given that I did it a fair bit. I have a dim memory of slipping eggs into boiling water to sit for a couple minutes, but I don't know. What I have done for years is to bring eggs in cold water to a boil, turn the heat off, and let them sit for 3 minutes. (For hard, sit for 15+.) That worked well.

Worked well with my old pot, anyway. Now I'm in a new place, with someone else's pots... so I tried making them against yesterday. "Bring to a boil" was a bit problematic, as the lid has a vent hole in it. And I let the eggs sit for four minutes because I got distracted. Result: eggs much closer to hard than soft, with no runny yolk. :(

I tried again today! I didn't even let the water come to a full boil, and waited exactly 3 minutes. Plus, instead of taking out each egg one at a time, I moved all three to a cold water bath before dissecting them. Result: some runniness, but yolks still partially hardened.

So I'm thinking the greater mass and size of the pot I'm using is a factor. Maybe there was something to the "slip eggs into boiling water" idea, though that has risks of splashing with boiling water, thus why I stopped.

Friends have suggested egg timers, though ones based on temperature sound more useful than simple timers. I can use a stopwatch just fine.