To remove orange peels, with a paring knife cut peels into lengthwise quarters, cutting to the surface of the fruit. Reserve fruit for another use. Pry back the quartered peel and pull away to remove. With a spoon scrape away the white pith inside the peel. (If pith is left on, peels will be bitter.) Cut peel into thin strips.
In a 2-quart saucepan combine the 1-1/3 cups of sugar, the water, and cayenne or rosemary. Cover and bring to boiling. Add orange peel strips. Return to boiling, stirring constantly to dissolve sugar. Reduce heat. Cook, uncovered, over medium-low heat. Mixture should boil at a moderate, steady rate over entire surface. Cook, stirring occasionally, for 15 minutes or until peel is almost translucent.
Using a slotted spoon, remove peel from syrup, allowing it to drain off of peel. Transfer peel to a wire rack set over waxed paper (discard rosemary, if using). Set cooked peel aside until cool enough to handle but still warm and slightly sticky. Roll peel in additional sugar to coat. Continue drying on the rack for 1 to 2 hours. Makes 48 pieces (about 1 cup).
Store, tightly covered, in a cool, dry place for up to 1 week. Or freeze for up to 6 months.