Cut the lime into small wedges and place into a Collins glass with the caster sugar.
Lightly muddle the lime, then stack the mint leaves and twist them to release their natural aroma. Rub the leaves around the rim of the glass, drop them in and lightly muddle to push the leaves into the lime wedges.
Half fill the glass with crushed ice and then pour in the rum. Muddle gently until the sugar has dissolved, then top up with more crushed ice and the soda water.
Garnish with a small sprig of mint leaves and serve.