1. Combine the lime juice, sugar, mango cubes, rum, Cointreau, and ice in a blender and process on high speed until completely smooth, 2 to 3 minutes.
2. Rub the rims of four to six stemmed glasses with the lime wedge. Then dip each glass in the superfine sugar to coat the rim, if desired.
3. Pour the daiquiri into the prepared glasses, and garnish each with a lime slice.
Yield: 4 to 6 servings