Place 10 fresh mint leaves and 2 teaspoons sugar in a sturdy glass or cocktail shaker.
Add 3 lime wedges to the glass.
Gently muddle mint and lime to release oils and juice without shredding the leaves.
Add the remaining 3 lime wedges and muddle very briefly to extract additional juice.
Pour in 2 oz (60 ml) white rum.
Fill the glass about two-thirds with ice (crushed or cubes).
Stir well to dissolve the sugar and chill the drink.
Top with 2–3 oz club soda to taste.
Gently stir once to combine without losing carbonation.
Garnish with a sprig of mint and a lime wheel; serve immediately.