In my case, they try and avoid general anesthetic...and I had my wisdom teeth out with (loads) of local. It was actually OK...and meant I got to go home straight away.
With me, my dentist referred me to the hospital...because he thought I needed a general, but the hospital said no, we try at all costs to treat T1 diabetis with local. I asked why...as being awake for the operation didn't sounds fun, and they told me that they could do a general, but it would mean a 24 hours stay in hospital...which was enough for me to go with the local! It could be, that your teeth are more "awkward" are will take more removing than mine, so it could be that general is the only option...but if you get a choice, I can say, that the local appraoch was absolutely fine.