Having your checking and savings accounts, along with other financial products like loans, at the same bank may provide benefits, such as preferred interest rates and fee discounts. But when you buy a “product bundle” at a bank—and you’re certainly pestered to do so—you don’t know whether you would have found a better deal if you had shopped around for the various parts.

Most likely you can save money by buying individual money products à la carte from different financial institutions. That’s what many subscribers in our survey already do. Half of those in our sample had a second bank or credit union. Almost two-fifths (38 percent) indicated that they were able to get better rates there for some services and products than at their primary bank or credit union. A case in point: 37 percent of subscribers who reported that they had loans relied exclusively on the second institution for them. And 41 percent of those with investment accounts at banks or credit unions had them only at their second financial institution, not their primary bank or credit union.

Where should you go for which products? We’ve designed this mix-and-match plan for maximum savings:

1. Open basic checking and savings accounts at a credit union that is a member of a network, such as the CO-OP system of 30,000 fee-free ATMs and 5,000 shared branches, and that provides online and mobile account access. Our survey found that credit-union customers were among the most highly satisfied overall. So start your search by checking the websites of the ones we rated to see whether you’re eligible for membership. If you don't qualify for one on our list, go to mycreditunion.gov and use the “CU Locator” in the toolbar at the top of the page. Comparison shop by following the links to credit-union websites.

2. Compare interest rates for certificates of deposit at the virtual banks we rated and at your credit union. Both types of institutions tend to pay the highest rates. But the best deal for the amount you plan to deposit and the length of time you need will vary based on the institution, whether you’re saving for the long term or short term, and on other details.

3. Choose a credit union for a car loan, because those institutions often offer the lowest rates—another good reason to join one. Get prequalified before you shop.

4. For credit cards and mortgages, shop online because the market for them is national, with lots of competitors, and you don’t want to limit your options by confining your search to, say, the bank where you have a checking account. For plastic, use a comparison site like creditcards.com; for mortgages, go to hsh.com. But check other sites to broaden your search. Bankrate.com provides rates for credit cards and mortgages, as well as auto loans and CDs. And if you’re a member of Costco, also explore the rates its mortgage lenders offer.

5. For brokerage services, shop first at one of the higher-rated firms in our most recent survey: Vanguard, T. Rowe Price, and USAA.

6. If you want a prepaid card, go directly to Bluebird, offered by Walmart and American Express, or Liquid from Chase. We rated both of them best among 23 reloadable prepaid cards evaluated in 2014 because of their low fees and terms. And both do almost everything that a checking account does.

7. Buy your paper checks from Costco or Walmart. You don’t have to get them from your financial institution; we found bargain prices at those two retailers. You can compare prices vs. the fees at your bank or credit union, and order online.

Editor's Note: This article also appeared in the January 2016 issue of Consumer Reports magazine.