Peel the oranges and slice them about 1/4" thick. Put a layer of 2 or 3 orange slices on the bottom of 4 deep individual dessert bowls. Sprinkle about 1 1/2 tablespoons sugar over each one, then sprinkle each with about 1 tablespoon grated coconut. Repeat the layers until you have used up all the orange slices. Cover with sugar and a layer of coconut. Set the bowls in the refigerator to chill for an hour or more before serving.

oranges, grated coconut, and confectioner's sugar.