In a blender container or food processor bowl combine the watermelon and the 1/3 cup syrup. Cover and blend or process until smooth. Press mixture through a fine mesh sieve into a medium bowl; discard pulp. Cover and refrigerate mixture at least 2 hours or up to 24 hours.

To serve, add ice cubes to ten 12-ounce glasses. Pour enough watermelon mixture into glasses to fill half full. Add enough carbonated water to fill glasses. If desired, sweeten individual servings with additional syrup; stir to dissolve syrup. Makes 10 servings. Watermelon Ice Cubes:Use these cubes to keep coolers cold without thinning outflavor. Cut 1-inch cubes from watermelon flesh. Place the melon cubes in a single layer in a 15x10x1-inch baking pan. Freeze for 1 to 2 hours or until firm. If storing longer than 4 hours, transfer cubes to a self-sealing plastic freezer bag or freezer container and freeze until ready to use.

Use these cubes to keep coolers cold without thinning outflavor. Cut 1-inch cubes from watermelon flesh. Place the melon cubes in a single layer in a 15x10x1-inch baking pan. Freeze for 1 to 2 hours or until firm. If storing longer than 4 hours, transfer cubes to a self-sealing plastic freezer bag or freezer container and freeze until ready to use.