I saw this recipe on food network and thought I'd try something like it. I had lychee juice in the fridge, so I used the recipe below as a guide and substituted lychee for cranberry. I also used 1/2 sugar and 1/2 splenda. I'll try all splenda next time and whatever juice on hand. Melik said it was the best desert ever!!

2 cups cranberry juice cocktail
1/3 cup sugar
1/4 cup fresh lime juice
1/4 cup vodka
6 fresh cranberries, for garnish

Whisk the cranberry juice and sugar in a heavy medium saucepan over medium heat just until the sugar dissolves. Pour the cranberry mixture into a 13 by 9 by 2-inch glass baking dish. Cool completely. Whisk in the lime juice and vodka. Freeze until the granita becomes slushy, about 2 hours. Using fork, stir to blend. Continue freezing the granita until frozen, stirring every hour to form crystals, at least 5 hours or overnight.
Divide the granita among 6 dessert glasses. Garnish with fresh cranberries, if desired, and serve.