Create simple syrup by combining two parts granulated sugar with one part water. Simmer, stirring, over low heat until sugar is dissolved. Chill before using.
Fill a shaker with ice.
Measure three tablespoons of sugar on a small plate. Run a lemon slice along edge of martini glass and dip in sugar to coat rim.
Add vodka, limoncello and simple syrup.
Shake well and strain into martini glass.
Garnish each with a lemon twist or slice.