Wash, peel, and cut the carrot in half lengthwise.
Wash the celery and cut into 2 or 3 short pieces.
Peel the onion and cut it in half.
Put enough water in the pan to cover the fish when you put it in.
Add the carrot, celery, onion, and parsley and turn on the heat to medium, covering the pan.
Five minutes after the water comes to a boil add the vinegar and salt.
When the water returns to a boil, add the fish.
Cook for about 10 minutes per inch of the thickest part of the fish, starting from when the water returns to a boil. The fish is done when it's moistly tender all the way through and has lost its pinkness next to the bone (if present).
Drain the fish. If using a whole fish, lift off and discard the skin while it's still warm and moist.
Brush the fish all over with olive oil.
Garnish with parsley, or lemon juice. Salt to taste.
Notes
This recipe originally called for wine vinegar, but migraine sufferers can get headaches form any vinegar except white distilled. I'm sure this is better with the right vinegar, but it tastes great as listed here.