headbutts are good.
The mistake with headbutts is to pull your head back, to get distance, then pull forward in an arc to gain momentum. Very bad idea. In real life situ's, when someone gets in your face, take a stance (footback for balance), tilt your head slightly down, and put your hand to your chin, like your interested in a discussion (your hand is there so there is very little distance to bring it out as a block for a variety of attacks). If the BG goes to headbutt you (they will inevitably pull their head back and ark down on you,),you will see their head tilt back at the start of their execution, tilt your face towards ground. They will connect their face on the top of your head...
In the face to face, if you know its gonna get ugly, from stance, bend legs, tilt face down, and push up in direction of BG's face. This may or may not connect with his face, but, it does get you inside very quick, and gives you oppertunity to get some thumbs up into their eyes, or push them off balance.
When your in so close, apart from knee to the groin, the best thing is to drop them to floor. Use a trip or side throw if you know the moves. If not, just keep pushing the forward momentum, after you've pushed up with the head; they will go over backwards. Sit on them, pull your head close to their head, so you wont take any big punches, go for they eye gauge, hold their head, and THEN you give them the headbutts. Once you have CONTROL of their head position, use your forehead on their face. At this close distance, punches too or from have very little power, and keeping low to opponent makes it almost impossible for them to throw you off. It will hurt you a little when you deliver, but believe me, just keep dropping them down, and you'll end up with a very cut, bloody and dissoriented BG. Once they're concussed, get up and deliver kicks, or kneel on them (safest, to make sure they cant get up) and give elbows or punches to aforementiond head/groin/throat/etc.