The day before, clean the ducks, remove all visible fat, and refrigerate, uncovered, overnight.
Preheat the oven to 550ºF. Remove the ducks from the refrigerator and with a fork prick the skin all over without piercing the meat.
In a bowl combine the 2 peeled tangerines with the sugar, and mash them with a potato masher until the sugar is thoroughly incorporated.
Using your fingers, lift the skin of each duck away from the breast meat and pack the pulp under each breast. Cut the 2 unpeeled tangerines in half, and rub the skin of the ducks all over with the cut sides of the fruit. Squeeze out the remaining juice from the halves, add to the tangerine/sugar mixture, and stuff the tangerine halves into the duck cavities. Pour half the remaining tangerine/sugar mixture into and over each duck.
Stuff each duck cavity with 1/4 cup of the onions, 1/4 cup of the celery, and 2 of the bay leaves. Sprinkle 1 teaspoon of the salt and 8 turns of the pepper over the skin and in the cavity of each duck; rub well into the skin. Sprinkle the reserved tangerine peels around a large roasting pan and place the ducks breast side up on a rack in the pan.
Roast the ducks for 20 to 22 minutes. Reduce the heat to 350ºF, and roast for 35 minutes. Turn the oven heat up to 475ºF, and roast until very dark and crisp, for about 20 minutes longer. Remove from the oven and drain the juices out of the cavity. Discard the juices.
To serve, cut off the wings at the second joint. Split each duck from the neck to the cavity, and serve one-half duck per portion.
Yield: 4 main-course servings