If desired, rim a martini glass by rubbing a lemon wedge around the edge, then dipping it into granulated sugar. Fill the glass with ice or place it in the freezer while you make the cocktail.
In a cocktail shaker, muddle the lemon and lime wedges until they release their juices.
Add the vodka, simple syrup, and a handful of ice. Cover and shake vigorously for 15–20 seconds, until well chilled.
Discard the ice from the prepared glass, then strain the cocktail into it. Garnish with a lemon twist or fresh mint, and serve immediately.
Notes
Coat the rim with sugar for the perfect sweet finish.
Shake vigorously to chill the cocktail and blend the flavors.
Fresh lemon and lime juice make all the difference.
Chill the martini glass before serving to keep the drink cold.