Add and muddle (use can use a muddling stick or a rolling pin) ½ lime cut into wedges, mint leaves and sugar syrup in a highball glass (or a solid base glass), until it becomes fragrant.
Add Ice and white rum to glass.
Fill glass to the top with either Lemonade or Soda Water (Lemonade will make the drink sweeter).
Garnish with a slice of lime on the side of the glass and a couple if fresh mint leaves on top.