Step 1Squeeze the juice from half a lime into the bottom of a glass. Add the mint leaves. Muddle the mint by crushing or mashing it with a spoon or flat-bottomed rod. The object is to saturate the mint with the liquid and loosely break up the mint. Don't destroy the mint. It should be broken up well, but gently.
Step 2Add three blackberries and muddle the berries. Add ice. The secret of a good cocktail is to pack ice to the top of the glass.
Step 3Add the rum of your choice.
Step 4Squeeze the juice of the remaining 1 1/2 limes into the cocktail. Add the simple syrup. Stir vigorously and top with the seltzer water (not 7-Up!).