Squeeze 4 lime wedges into a large Collins glass (or highball), then drop into glass. Add 3 level bar spoons sugar, 1 ounce club soda, and fresh pineapple.
Use muddler to press and twist the ingredients together a few times. (Do not pulverize ingredients ... there should still be some small chunks.)
Stack mint leaves in the palm of your hand. Smack leaves with your other hand, 5 to 6 times, or until fragrant.
Rub mint over glass rim, then drop into drink.
Add pineapple juice and rum to drink, then fill glass with ice, leaving about an inch at the top. Top off drink with club soda.
Mix drink well, using bar spoon.
Serve immediately, garnished with a sprig of mint and a pineapple wedge, if desired. Enjoy!
If you'd prefer, you can make this drink in a cocktail shaker instead of a glass. Prepare as directed (stir, do not shake) in the cocktail shaker. Then to serve, transfer the drink to your glass without straining.