Frozen Watermelon Margarita

2 1/2 cups seedless (or seeded) watermelon, cut
    into 1-inch cubes, rind discarded before measuring
3 tablespoons freshly squeezed lime juice
4 ounces tequila (ideally, an aged tequila)
2 ounces Cointreau or triple sec
1 1/2 cups ice

Put cut watermelon in a plastic bag and place in freezer for a minimum of 2 hours. (If time does not permit this step, add a few extra ice cubes when blending the difference is not that significant.)

Stuff all ingredients into a blender and puree until smooth. Garnish with a watermelon wedge and serve immediately.