HAHAHAHAHAHAHA!!!
I guess don't knock it till you try it... but what about that little ribbon around the foot of an Anejo? You supposed to smoke thru that too? :p
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I haven't had many cigars with a cedar sleeve, but I do remove my cigars from the cellophane. I'm not sure if that makes any difference, because cellophane and cedar are both supposed to breathe.
Edit: I did see a neat trick once where someone lit their cigar using the cedar sleeve. They slid it down about 1.5" and lit it. Took a few puffs and it lit the cigar pretty well. Eventually he blew out the sleeve and slipped the remaining bit off into the ashtray.
I've got about dozen Anejos in the humidor and some of them have been there a couple years. I sure hope it doesn't hurt them.
I leave them on and use them to light the cigar.