In a small saucepan, dissolve Splenda in water. Bring to a boil. Boil for 2 minutes or until slightly thickened. Place in sealed container and refrigerate until chilled. Use 3/4 oz for recipe and reserve rest for later use.
In a tall glass filled with ice, add simple syrup, lemon juice and Gin. Stir well. Top with club soda. Add a lemon wedge for garnish if desired.