Cut each lime in half crosswise, then cut each half into 8 pieces. Place 12 pieces of lime in each of four double old-fashioned glasses (or other 12-ounce glasses). Sprinkle 2 tablespoons of the sugar into each glass. Using a muddler (or the butt end of a large wooden spoon), mash the limes into the bottom of the glass until the sugar is dissolved, stirring occasionally. Fill each glass with 1 1 /2 cups of the ice and 1/4 cup of the cachaça. One glass at a time, transfer the contents of the glass to a cocktail shaker, and invert the glass over the shaker to act as a lid. Shake the glass and shaker together to combine the sugar and cachaça, shaking until well chilled. Lift the glass from the shaker, and pour the contents back into the glass. Repeat the process with the remaining three glasses.

Garnish with a slice of lime or a sugarcane swizzle stick, if desired.