Place 1 teaspoon of sugar into each of two 12 ounce glasses. Squeeze the juice from a lime wedge into each glass, drop in the wedge, and add 2 sprigs of mint. Use a spoon or muddler to mash the sugar, lime juice, and mint together in the bottom of the glasses. Fill each glass about half full with crushed ice.
Pour 1/4 cup rum into each glass. Fill the glasses with club soda, stir, and garnish with additional lime wedges.
