I may be one of the few people of my generation who has never had so much as lit a cigarette. When I was required to carry one in a theatrical production, someone had to show me how to hold it. How was I to know one didn't use the thumb and index finger?
One doesn't? *confused* Sorry, I don't know. I never smoked in my life, and I don't intend to start now.
As far as I knew (from growing up in a family where my dad, mum, two uncles, and one grandfather smoked), you hold it with your index and middle fingers ... and when the thing starts getting small, you use your thumb and index finger. :-\
Maybe I'm wrong, but that's how I always saw people do it.
P.S. Granddad died from cancer before I was 2 and one of my uncles died from emphysema before I was 10.
