Place all the ingredients in a blender. Add 4 cups cold water and blend on high speed until limes are slightly chopped. Strain into a pitcher and then, with the strainer still resting above the pitcher, slowly pour about 1 more cup water (depending on how sweet you want the drink) through the strainer over the lime pieces to extract all the residual sugar and juice.
Note: Nutritional analysis is per cup.
Strain out the lime rinds so the lemonade won't get bitter.