In a sturdy glass, add the mint leaves and lime wedges. Use a muddler or the back of a spoon to gently mash them together, releasing the mint oils and lime juice.
Sprinkle the sugar over the muddled mint and lime, and stir well to combine.
Fill the glass with ice cubes to the top.
Add the white rum over the ice.
Fill the rest of the glass with soda water, stirring gently to mix.
Garnish with additional mint leaves and a lime wedge, if desired.
Serve immediately and enjoy your refreshing mojito!