I always keep the band on, Uncle gave one reason, nothing worse than tearing the wrapper getting it off. But I also like to study my cigar while smoking it, and like to look at the band, and it is not for ego as I almost always smoke alone. I also like to hold the cigar over the band and keep my grubby fingers off the wrapper, after all the cigar band was created so Catherine the Great wasn't it?, wouldn't have to touch the cigars with her royal fingers.