That is it, my friend. I really believe in taking the right hook (from the southpaw) out of the game, make him throw the left and counter it. Of course, as you said, the mirror image is equally true.
Something that I've read about and been told about (never heard about it my active days- my weapon of choice against southpaws, besides the nosebleed, was the right uppercut. I tried the draw the left and counter trick- hence the nosebleeds- but my slipping skills...that wasn't my game...didn't allow me to use my hook as a counter like I would've liked. Do it all day against a jab-slip outside and hook. I truly believe that, at some levl, and if you let them, lefties can hypnotize you.