In a large glass or cocktail shaker stir together lime juice and sugar until sugar has dissolved. Add mint leaves and a few slices of kiwi and muddle until fruit and mint are crushed and fragrant.
Add rum and a handful of crushed ice and stir until combined.
Fill four small glasses with crushed ice. Add mint sprigs, kiwi slices and lime wedges to each glass.
Divide the cocktail between the four glasses, top each glass with club soda. Add a straw and enjoy immediately.