Toss the ice in the blender. Add the gin, lemon or lime juice, and sugar and blend until smooooooth. (You may need to pulse it several times at the beginning until the ice is properly chopped. And then let the motor whir even if the blender begins to hop a little.)
Pour the boozy concoction into a glass. Top with a splash of soda water (or, for a sweeter twist, some lemon-lime soda). Garnish with the lemon or lime.