I believe you are not looking for an alternative bank; you are looking for an alternative currency. The Federal Reserve gives explicit rights to private banks to not have to worry about whether the US Dollars in their possession are 100% backed up by actual reserves of US Dollars. In fact, they encourage banks to not be able to pay you back, through fractional reserve banking, if everyone were to withdraw their deposits. The Federal Reserve has a complete monopoly over how the US Dollar is managed in electronic form. I'm not even sure that a bank that refuses to participate in fractional reserve banking will be allowed to operate, or at least that you will be covered by the official deposit guarantee in case they go bankrupt. I realize there really are no alternatives, which makes my advice somewhat useless, but by using US Dollars (or any other state paper currency) you are supporting the current monetary system (which includes the private banks).