Fill a cocktail shaker with ice cubes. Add the gin, lime juice, and simple syrup to the shaker.
Shake the concoction vigorously for 15–20 seconds to thoroughly mix and chill the cocktail.
Strain the cocktail into a chilled coupe or martini glass to remove any ice or sediment.
Garnish with a lime twist (i.e., twisting a strip of lime peel over the glass to release the aromatic oils) or a lime wheel.