Americans are saving more. But where are people putting all their cold, hard cash? It's getting tougher to find a bank where you won't end up paying to keep your money safe.

The average interest paid on savings, checking, money-market and certificate of deposit accounts fell to 0.99 percent in July, the first dip below 1 percent in a decade, according to Market Rates Insight. Banks are also raising fees and adding new ones, some in response to the financial-services overhaul bill that became law July 21.

The result? More savers are seeing their deposit earnings eaten up by charges. And it may be cheaper to stuff your money under a mattress then to stick it in the bank.

One recent example: A Chase savings account with a 0.01 percent interest rate. With a $10,000 deposit the account would make about $1 in annual interest. Now consider the potential fees: $4 if the balance fell below $300, $2 for non-Chase ATM withdrawals and $3 for each withdrawal over 4 per month.

If you know you won't need the money immediately, you might take a look at CDs, which pay greater interest depending on the length of time you agree to keep your money locked away. You won't make a ton more than a savings account, but every little bit helps, right? Online banks, money-market funds, Treasuries and savings bonds are other options.