1. Wash the fish trimmings in a deep bowl set under cold running water. Drain, and then mash the pieces of fish with the back of a large spoon.
2. Place the mashed fish in a 3- to 4-quart enameled or stainless-steel saucepan and pour in the water. Bring slowly to a simmer over moderate heat and cook uncovered for 5 minutes, skimming off the foam and scum as they rise to the surface.
3. Add the onions, celery, bay leaf, thyme, salt and peppercorns, and reduce the heat to low. Simmer partially covered for 30 minutes, skimming the surface from time to time.
4. Remove the pan from the heat and, with a slotted spoon, lift out and discard the fish and vegetables. Strain the stock into a deep bowl through a fine sieve lined with a double thickness of dampened cheesecloth.
5. The stock will keep refrigerated for 2 or 3 days or it can be cooled to room temperature, covered tightly and frozen.
