I had a LEEP done a few years ago. Basically the doctor uses an electrode with a loop on the end to remove a segment of the cervix. It can be used to perform a biopsy on suspicious tissue, or can be used to remove tissue that may be pre-cancerous. My gyn did mine in the hospital as an outpatient procedure, and I was under general anesthesia for it. It only took a short while for the procedure, so I wasn't really under very long, woke up completely alert, and went home an hour later. I was told there might be some bleeding afterwards, but I didn't have any, and had no pain at all. I believe they can also be done with just local anesthesia, but I don't know if that would involve any pain at all. Personally, I liked being totally out for it. It was over before I knew it.
I know nothing about Leeps - there are cervical procedures, you might want to try the women's health forum. Someone there might have an answer for you