If you would like salt-rimmed glasses, begin by running a lime slice (the juicy part) around the top rim of a glass.  Fill a shallow bowl with salt, and dip the rim of the glass in the salt to coat with salt.  Set aside.

Add tequila, Cointreau, lime juice, mint sprigs and a few ice cubes to a cocktail shaker.  Using a cocktail muddler or the end of a wooden spoon, muddle the mint briefly.  Cover and shake vigorously for 10 seconds, or until the drink is chilled.  Then give it a taste, and add in extra sweetener or mint if desired.

Fill your serving glass with ice.  Pour in the margarita mixture over the rocks.  Serve immediately, garnished with an extra lime wedge and/or sprig of mint if desired.