In a small saucepan, combine the raspberries, vanilla sugar, and 1 cup water and bring to a boil over high heat, stirring until the sugar has dissolved.

Remove from the heat and strain through the sieve placed over a small bowl to remove most of the raspberry seeds. Add the lemon and lime juices to the raspberry syrup and stir to combine.

Chill the syrup before using.

For each drink, pour 2 tablespoons syrup and 1.5 oz of vodka into a tall glass filled with ice. Top with soda water, and garnish with fresh lime slices before serving.