Using the point of a sharp knife, cut the peels of the oranges, tangelos, or tangerines into quarters. Using the bowl of a spoon, loosen the peel from the pulp and membrane of the fruit, leaving the white pith attached to the peel. (Save the pulp of the fruit for another use.)
Place the fruit peel in a 2-1/2-quart microwave-safe bowl Add enough cold water to the bowl to cover the fruit peel. Weight the peel down with a plate, if necessary, to keep the peel under the water. Let the fruit peel stand overnight weighted down in the cold water.
Drain the fruit peel; rinse it thoroughly in cold water. Place the fruit peel in a 2-quart saucepan. Cover the fruit peel with fresh cold water and heat to boiling. Remove saucepan from heat; let stand 10 minutes. Drain fruit peel. Repeat the boiling and standing process three more times. (This help remove the bitter taste from the peel.) After draining the fruit peel for the last time, let it stand until thoroughly cooled.
With kitchen scissors, cut the cooled fruit peel into strips about 1/4 inch wide. In a saucepan combine the 2 cups sugar and the 1/2 cup water. Cook over medium-high heat to boiling, stirring constantly with a wooden spoon to dissolve sugar. This should take 5 to 7 minutes. Carefully add the fruit peel strips to the saucepan.
Cook over medium-low heat, stirring occasionally, until fruit peel is translucent and most of the liquid is absorbed. Mixture should boil at a moderate, steady rate over the entire surface. This should take 25 to 30 minutes.
Drain the fruit peel thoroughly; cool to lukewarm. While peel is still slightly sticky, roll it in the additional sugar to coat. Place coated fruit peel on a wire rack for 1 to 2 hours or until dry. Store tightly covered. Makes 16 servings (about 4 cups).