Put the lime wedges, the rinsed blackberries, sugar and rum in a shaker or a glass, and muddle everything well, – ideally with a muddler.If your blackberries are on the tart side, I recommend using 2 tbsp sugar.
Add the mint leaves and press/bruise them lightly so they release their oils, just a couple of times with the muddler, – don't crush them too much.
Fill 2 glasses with ice, preferably crushed ice, – and divide the mixture between the glasses.Don't strain the liquid. There is plenty of flavour in the lime wedges, the crushed blackberries and so on, - and it looks beautifully rustic.
Stir well with a spoon so everything is thoroughly mixed with the ice, and top up your blackberry mojito with soda water.
Garnish with fresh blackberries and a little mint, if you like.