Using a trussing needle or sharp skewer, pierce each cranberry completely through. In a 2 to 3 quart (2-3 L) enameled or stainless steel pot combine 3 cups (750 g) of the sugar and the water. Cook over moderate heat, stirring constantly, until the sugar dissolves. Raise the heat and cook briskly for about 5 minutes, until the syrup reaches a temperature of 220F (105C) on a candy thermometer, or 8 degrees F (5 degrees C) above the boiling point of water in your area. Remove the pan from the heat and CAREFULLY (the syrup is very hot) stir the cranberries into the syrup, turning them gently with a spoon until the berries are thoroughly coated. Set aside at room temperature for 12 to 24 hours.
Stirring gently, bring the cranberries and syrup to a simmer over moderate heat. Drain the berries in a sieve or colander and return the syrup to the pan. Bring the syrup to a boil over high heat and cook uncovered and undisturbed until it reaches 250F (121C) on a candy thermometer, or until a few drops of the syrup form a firm but pliable ball when dropped into water. Remove the pan from the heat and CAREFULLY drop the berries into the syrup, stirring to coat them thoroughly. Using a slotted spoon, arrange the berries in a single layer on wax paper, discarding the remaining syrup. Let the berries cool to lukewarm. If little puddles of syrup form around the berries, carefully move them to a clean part of the paper. Roll the berries two or three at a time in the remaining cup (250 g) of sugar and cool to room temperature, or refrigerate before serving.