A Half Counihan, as opposed to the Full Counihan occurs when only of the sexual partners is drunk enough to vomit during the sexual act, but not both. Addtionally, the man, or if the partners are gay men, one of the men, must finish by jacking off on their sexual partner.
Jack pulled a Half Counihan on Jill last night. They were both bombed last night and having sex. Jill, however, was really blacked out and threw up on the bed. Still, Jack wasn't finished so he jerked off on her.