Place the blackberries, simple syrup, and lemon juice into a cocktail shaker. Using a muddler (or the back of a wooden spoon), thoroughly mash the ingredients, allowing the blackberry juices to release.
Add the rum and three ice cubes to the cocktail shaker. Tightly seal the lid onto the cocktail shaker and shake vigorously for 45-60 seconds.
Strain the blackberry cocktail into a double old-fashioned glass. Top with additional ice. Garnish with a lemon slice and straw if you like. Serve immediately.
