Combine sugar and water in a small saucepan. Bring the mixture to a boil and continue to boil, stirring, until the sugar is dissolved, 2 to 3 minutes. Remove from heat and let cool completely.
The cocktail:
Fill a cocktail shaker halfway with ice. Add lime juice, vodka, triple sec, and ¾ oz. simple syrup. Shake well, about 15 seconds, to chill the mixture. Strain into a highball or martini glass for a single drink or, if you prefer, into 4 separate shot glasses. Garnish with a wedge of lime and serve cold.