Combine clementine juice, sugar, and rum, if desired, stirring to dissolve the sugar. Adjust the sweetness with more sugar if needed. Pour mixture into a 9-inch square pan or dish and freeze, stirring and crushing lumps with a fork every few hours, until frozen, 4 to 6 hours. Serve in hollowed out clementine rounds, if desired.
Yield: 6 to 8 servings