A massive thank you to infonote over at the Digital Point Forums for pointing me in the direction of something called section targeting. Basically what it does is highlight which parts of your page you want AdSense to read when it’s deciding which ads to display. You can also chose which parts of your page you want AdSense to ignore.
Brilliant! Absolutely brilliant! However it has made me realise that I ought to spend some more time looking through the AdSense Help Center (grrr…I hate spelling in American)