Whatever you think about JPMorgan Chase's (NYSE: JPM) deal to buy Bear Stearns (NYSE: BSC) for a couple of bucks, one thing seems clear: Bear Stearns investors dodged a bullet on Sunday. Whether you want to believe it or not, this bank nearly went 'rupt.

There's simply no other explanation for Bear's board approving the $2-per-share sale of a firm that, by its own estimation, has $84 a share in book value. These guys were scared.

Should we be, too?
I don't know necessarily that we should be scared, but I'll be honest with you -- I've done my share of tossing and turning the past few months, wondering about the what-ifs and pondering the should-I-maybes.

Rumblings over the liquidity of America's leading banks and brokers began in October 2007, and quickly proved well-founded in November, when E*Trade (Nasdaq: ETFC) had its near-death experience. Not long after, we saw Citigroup (NYSE: C) slash its dividend and Bank of America (NYSE: BAC) play white knight to Countrywide (NYSE: CFC). But as serious as all of these crises seemed at the time, none provided quite the shock to the financial system that Sunday's news did. Sure, Bear Stearns looked sickly on Friday, but few people realized just how bad things might have become had JPMorgan not made its play on Sunday. The Washington Post minced no words describing one what-if: "A complete collapse of Bear Stearns might have crushed the already-dwindling confidence in the global financial system ..."

Indeed. And it gets worse. You know how they say that when one person dies, it's a tragedy, but when 1 million people die, it's a statistic? Well, things work a little differently in the stock market. When one firm goes bankrupt, it's a hit to an investor's well-diversified portfolio. But when that firm is a broker, and an investor has all his savings with that now-bankrupt broker, that's a real tragedy. On Sunday, Bear Stearns clients came face to face with the nightmare possibility that their broker would go bust, perhaps taking their assets with it.

Wake up
Now, most investment professionals (and Jim Cramer, too) will tell you that losing your savings in a bank default is an unreasonable fear. By law, Bear Stearns and its brother brokers -- everybody from discounters like TD AMERITRADE (Nasdaq: AMTD) to ritzy Goldman Sachs -- are required to keep client assets separate from their own, and to maintain sufficient funds to allow their customers to redeem securities from their accounts at any time.

But the thing about unreasonable fears is that they're ... unreasonable. Telling you something isn't supposed to happen doesn't really address the concern: "But what if it does happen?" So let's address that now with a few clear steps you can take to protect your nest egg(s) from the what-ifs.

Few eggs, all in one basket
In the simplest what-if scenario, say you've got $100,000 or less in savings, and it's all in savings, checking, or CDs, at a single bank. Here, you're just about as safe as safe can be. Assuming your bank is "FDIC-insured" -- and almost all are -- then the Federal Deposit Insurance Corporation has your back. You are insured up to $100K, cash. And if you're married and have a joint account with your spouse, the two of you are covered up to $200K.

If you're in the fortunate situation of having more cash than that, then consider moving some of it to a second bank, where your new account will be separately insured, again up to the $100,000 or $200,000 limit(s).

More eggs, more baskets
Things get only a little more complicated if you have both cash and stocks, with all the cash at one bank, and all the stocks with one broker. Your cash in the bank is subject to the above rule. As for the stocks, they're insured separately by the Securities Investor Protection Corporation -- and may be doubly insured if your broker has taken out a separate insurance policy with a private insurer (every broker's website that I've reviewed so far does have additional insurance, often from Lloyd's or CAPCO). The SIPC will make sure you get your stocks back (eventually) if your broker goes kaput, somehow taking your account with it, refunding you up to $500,000 in losses. Additional insurance could cover even more than that.

If you've got more than $500K, then here's the deal: Apply the above rules to protecting your cash in the bank. For your broker, either confirm that it has insurance over and above what SIPC guarantees, or open a new brokerage account with another broker (or several, if you're really well off), and keep your head down below that $500,000 threshold at both (or several) brokers.

No fair laying more eggs
Now for two ideas that will not work, and that you should rule out. First, SIPC is not FDIC, and the rules for the two differ. For one thing, no fair doubling up at SIPC. A joint account owned by husband and wife is still insured up to "just" $500,000.

Also nixed is the idea of opening new accounts with the same bank/broker. Splitting up your funds in that manner won't cut it -- with a few narrow exceptions (e.g. opening a separate trust account for a third person) they'll all get lumped back together for purposes of figuring how much is insured.

Foolish takeaway
So the short answer on how to protect your assets in the event that your bank goes 'rupt is this: The more eggs you have, the more baskets you want. Anytime your cash surpasses $100,000 per person at a bank, find yourself a new bank, open an account, and start filling it up. Same deal for brokerage accounts and $500,000. While this will increase your paperwork at tax time, and increase your record-keeping burden all year long, having the peace of mind will be worth it.

For further Foolishness on the subject of broker bankruptcy, read:

Bank of America and JPMorgan Chase are Income Investor recommendations.

Fool contributor Rich Smith does not own shares in any company mentioned above. The Motley Fool's disclosure policy is FOOL-insured.