Mix the raspberries, sugar and water in a small saucepan over medium heat. Stir until all the sugar is dissolved and the syrup is bubbly. Remove from heat and allow to cool slightly.

Put the syrup through a sieve to remove the solids. Chill the syrup to room temperature.

Next, put the raspberry simple syrup, rum, lime juice, lime wedges, and mint leaves into a cocktail shaker. Muddle in the shaker. Put on the shaker lid and shake to combine.

Fill 2 glasses with ice. Open the shaker and pour half the liquid into each glass, including the mint and lime wedges. Fill the rest of the glass with soda water.

Garnish with a few raspberries and a sprig of mint. Serve.