Place the blackberries, raspberries, mint leaves and 2 lime wedges in a highball glass.
Add the simple syrup and muddle firmly for about 15 seconds, until the berries break down into a rough puree and the mint smells bright.
Squeeze in the remaining lime wedges and drop the rinds into the glass.
Fill the glass with crushed ice.
Top with the club soda and stir once from the bottom to lift the fruit through the drink.
Garnish with a skewer of whole berries laid across the rim.
Good to Know
Muddle the berries, mint and lime for the whole group ahead of time and divide between glasses right before serving, so the fizz never has time to flatten.