Wash the herrings well; clean, scrape, and cut off the heads, tails and fins. Rinse several times in cold water until water is clear. Cut the fish into 1-inch pieces. Place in layers in a crock with the onions, horseradish, carrot, spices and bay leaves between the layers.
Heat the vinegar, sugar and water just to the boiling point. Let cool. Pour over the herring. Press down firmly with a plate, putting a weight on top, and let stand in refrigerator about 6 days.