In a small bowl, combine sugar, salt, caraway seeds and dill, and mix well. Sprinkle the bottom of a large dish with a handful of cure. Place a layer of fish skin side up, then sprinkle with more cure.
Continue with the rest of the fish. Cover, place in refrigerator and let sit for 1 to 2 days. To serve, scrape of the dill, and slice the fish thinly. Sprinkle with fresh dill and serve with bread and mustard.