"harsher/bitterness" usually comes from smoking to fast. If Im reading a book while enjoying a cigar I usually read a page, take a puff read another page take another puff.
I will only add: Slow down on your smoking pace, get the best cigars you can afford and try many. Once you find your go to sticks you can try others from that maker and go from there. I kept/keep a cigar log. When I first started I logged every single one I lit and wrote what I liked and didn't, gave it my own STAR rating per say.
Now I more or less log the new ones I try that are really good or really bad for future reference.