1. Bring 1 cup water and sugar to a boil in a medium saucepan. Boil, stirring often, until sugar dissolves. Remove from heat; add mint sprigs, and let stand 2 hours or until mixture is completely cool.
2. Pour mixture through a wire-mesh strainer into a pitcher, discarding mint. Stir in lemon-lime soft drink, lime juice, and tequila. Serve over ice. Garnish, if desired.
The simple syrup needed for this beverage may be made up to 1 week ahead and stored in the refrigerator.