How do I balance the bitterness of raddichio in soup?
Was the radicchio fresh? I'm not a big lettuce fan but I know a lot of greens can be bitter fresh (mustard greens, collards, calaloo) and can benefit from steaming, boiling or cooking first. 

Actually this website has a load of tips for reducing the bitterness in greens: http://www.justhungry.com/counteracting-bitterness-greens