Combine 1 cup water and sugar in a small saucepan. Bring to a boil over medium-high heat; reduce heat, and simmer 3 minutes, stirring until sugar dissolves. Remove from heat; stir in lemon and orange rind strips. Transfer rind mixture to a bowl; cool 10 minutes. Cover and refrigerate 30 minutes or until thoroughly chilled. Remove and discard lemon and orange rind strips. Stir in juices.
Pour into an 8-inch square glass or ceramic baking dish. Freeze until partially frozen (about 1 hour). Scrape with a fork, crushing any lumps. Freeze, scraping with a fork every 45 minutes, 3 hours or until completely frozen. Spoon mixture into chilled glasses or bowls.