Lime drink: In a pitcher combine the water and syrup or sugar, stirring to make sure the sugar is well dissolved. Refrigerate til very cold.
Just before serving, grate the rind of the lime into the pitcher, being careful not to include any of the white part. Serve over ice cubes.
Simple syrup: Combine the water and sugar in a small saucepan. Heat gently, stirring constantly, til the sugar is completely dissolved. Bring to a boil over medium heat and cook til reduced to 1 cup. Let cool to room temp.; store, refrigerated, in a tightly covered container.