In a cocktail shaker, combine mint leaves, lime juice and sugar. Muddle the mint using a cocktail muddler to release the flavor - but not so much you rip them apart into a bunch of tiny pieces.
Add rum and about 1 cup of ice cubes, cover the cocktail shaker and shake for 10-15 seconds.
4 ounces white rum, Ice cubes
Fill two 12 or 16 ounce highball glasses with ice cubes, then strain the mixture evenly into the glasses. If the mint didn't pour out on it's own, spoon them out of the shaker and evenly distribute them between the two glasses, pushing them down into the drink with a spoon. If you sliced your limes into wedges, you can add a few of those to each glass as well.
Top with a splash of club soda and a fresh mint spring to garnish. Add straws, serve and enjoy!