Rinse the fillets in cold water and pat them dry with paper towels.
Crush the caraway seeds, aniseed, juniper berries, red pepper flakes, and black peppercorns using a mortar and pestle. Or place the spices on a cutting board or other hard surface and crush them with the underside of a heavy skillet. Combine with the salt, sugar, and dill.
Place one of the fillets skin side down in a deep dish just big enough to hold the fillets. Rub the fillet with half the spice and dill mixture. Rub the other fillet with the mixture and place it skin side up on top of the first. Pour the aquavit on top, cover the dish with plastic wrap, and place a heavy weight, such as two heavy plates or a saucepan, on top of the fish.
Refrigerate for 3 to 4 days, turning the fish every 12 hours and basting it with the brine that accumulates in the dish.
To serve, dust off some of the spices and slice the fish into thin slices with a sharp thin knife. The flesh from the tail will be leaner than the flesh from the belly. Serve with mustard sauce and dark rye bread, for open-faced sandwiches, or with mustard, pickles, and capers.
Serves 6 to 8