I hate doing that. I ended up with a duplicate card. Learned the hard way how a duplicate CC got me in trouble. I use to like keeping one CC in my car for gas, another in my wallet. Someone spotted that I had 2 CCs with identical numbers and stole one. As far as I knew I still had it, used it all the time. They ran up fraud charges on the duplicate one thinking I'd not notice and pay the bills. Had I only had 1 CC I would have known it was missing and canceled it.
So being that the CC company sent me a duplicate I needed to shred the old one. It just felt wrong to destroy something that I worked so hard to get even if they sent me a duplicate.