Please forgive the truly newbie question, but...

What is most commonly done about the dark-foul-sour after-taste that usually follows a cigar?

I have tried different beverages (libations!) with them, and that seems to REDUCE, but not ELIMINATE such after-taste.

I have also tried not consuming the entire cigar; letting it dwindle somewhere beyond the half-way point so as not to go down to the literally "bitter end."

All to no avail. Suggestions?