Pour the water into a pitcher, add the agave syrup or sugar mixture, and mix well.
Squeeze the juice from the lemons and limes into the pitcher, reserving the spent citrus halves. Taste and, if desired, add agave syrup or sugar according to taste.
If desired, slice 2 squeezed lemon halves and 4 squeezed lime halves in half again (by our count, that makes 12 wedges) and toss them in the pitcher.