I don't have a Costanza. link
With my cell phone taking over most of the duties that used to be done by my wallet, I've slimmed my wallet down to tiny dimensions. I have my license, 2 credit cards, two of my business cards for handing out (I keep extras in my car and in my computer bag), and a bit of cash. I have a super-thin, super-simple wallet that is basically two business-card-size pockets hinged together, and it's only about 3/16" thick.
As more and more businesses get NFC readers for checkout, I won't even need to carry the credit cards, and more and more, I'm just sending my "business card" to people via email as a .VCF file. That's why I only keep 2 paper cards with me.
My Nexus 4 replaces credit cards, loyalty/discount/rewards cards, business cards (I can take a picture of a card and have the data imported into my Contacts), photos, To-Do lists, grocery lists, calendar/schedules, and lots more. All that stuff I no longer have to carry around on paper/plastic, so dealing with a wallet is easy.
I *do* know guys who still carry Costanza wallets, and yeah, I promise you they are sitting sideways and probably have back problems.