Using a paring knife, cut 6 slits from top to bottom of each citrus fruit, cutting through peel but not into fruit. Using your fingers, gently remove peel. Reserve fruit for another use. Using a paring knife, remove excess pith from peel, and discard. Slice each piece of peel lengthwise into thin strips, each about 1/8 inch wide.
Place citrus-peel strips in a large saucepan, and cover with cold water. Bring to a boil, then drain. Repeat twice (boil three times in all).
Bring 3 cups sugar and the 3 cups water to a boil in the saucepan, stirring occasionally until sugar dissolves. Stop stirring; wash sides of pan with a wet pastry brush to prevent sugar crystals from forming. Add strips to boiling syrup, reduce heat to medium-low, and simmer gently until strips are translucent, about 30 minutes. Remove pan from heat, and let strips cool in syrup. (Strips in syrup will keep, covered and refrigerated, for up to 3 weeks.)
Using a slotted spoon, transfer strips to a wire rack placed on a rimmed baking sheet. Let liquid drain and dry off, about 30 minutes, then roll strips in remaining 1 cup sugar. Let dry in a single layer on a wire rack at least 30 minutes. Sugared peels will keep, covered at room temperature, up to 2 weeks.