I use two actually (at the same time). One contains my IDs and most of my credit cards and is very thin (a card case). The second is a bifold with a separated cash pocket so I can carry both dollars and yen without mixing them. I have one credit card in there plus all the other junk that goes into a wallet. The theory is that if I'm ever robbed, I can give them the big wallet and won't lose all that much (the CC is my AMEX).
Not too worried about being robbed in Japan, but it's a habit I got into. I used to carry a card case and a money clip, but the money clip wouldn't work with dollars and yen together (too confusing and clumsy).