If you were to add granulated sugar, you'd have a gritty drink that promotes tooth decay. Sugar doesn't dissolve well in alcohol, nor in a chilled drink. To make your own simple syrup, dissolve two cups sugar in one cup water, until the water boils. The longer you boil the water, the stronger the syrup. Bottle your concoction in attractive container so it doesn't look so simple.
Most drinks call for one teaspoon of sugar, and every batch of simple sugar is different.
If you've reduced your sugar to the viscosity of dragster motor oil, your use of it should reflect this. Remember, the idea is to sweeten the cocktail, not induce a diabetic coma. Wash the lime and cut it into quarters. Place the lime pieces in the bottom of a chilled tumbler pulp-side up. Pour the simple syrup over the lime and muddle.