For each drink: In a highball glass, use a muddler (can also use a fork) to crush 2 tablespoons of blueberries, 1 lime slice, 2 teaspoons of sugar and 3 mint leaves.
Fill a cocktail shaker with ice, add the rum and shake for 30 seconds.
Pour the rum into the glass and top with approximately 1/3 cup sparkling water, 1 and 1/2 teaspoons lime juice and additional ice cubes.
Repeat with remaining ingredients to make 4 drinks
Garnish with additional blueberries, mint sprigs and lime wedges if desired.