Hi Wisniak. I can carry alot more than 4 bills in my secrid. I havn't tested how many, but I often have up to 6 in there and haven't noticed any issues. But then they are folded of course - you can't place unfolded bills in a wallet that small - I most often use English pound notes and they are are alot larger than dollar bills.
Have you had a look at All - ett wallets. I'm fairly sure they'd have something that would fit the bill. Regards. Dave