Plebian is our resident expert on medieval weapons. He knows a great deal about the subject, including halfswording...
I have a cousin who is a member of the Creative Acronisum (sp?) Society, a group who gets together to beat the snot out of each other with Oak staves as swords while dressed in homemade but period correct armor.
I have an interest in edged weapons so I asked cousin Chris to bring an extra set of armor next time he was coming to town and he did. We faced off and he was awesome. I'm pretty agile, but he was able to stand in front of me and whack me repeatedly in the back of the helmet with his Oak "sword". I had no defense for this and ultimately had to strike his sword hand (cheating) to make him drop his "sword". I promptly stepped on it and held my sword in high ready.
He could have charged me weaponless, but this was a friendly fight so he just b____ed about me cheating. Moral to the story, chivalry aside, there are no rules in a real fight, take any advantage you can. Of course if it were a real sword fight with real swords he would have cut my head off long before I had a chance to strike his sword hand.