I'm trying to figure this out now myself (before I even have sex). Maybe I'm thinking of this the wrong way, but I see unprotected sex as having two factors: the risk of STDs and the possibility of getting pregnant.
I am a virgin, so there's no way I have anything, but my guy is not. If he gets tested for STDs and has nothing and I'm on the pill (to cover the pregnancy aspect of the situation) would a condom still be necessary? Granted, I'm aware the pill doesn't always prevent pregnancy but, theoretically?