Americans are getting better at saving: 58% have more money than they owe in credit card debt

Suze Orman explains how much money you'll need to have when an emergency...

The Federal Reserve announced recently that outstanding credit card debt in the United States hit a new high: $1.02 trillion, an increase of $11.2 billion since its last count. According to one estimate, the average U.S. adult owes nearly $6,000. Still, according to a new survey from financial website Bankrate, some Americans prioritize another financial task over paying down that debt: Building up their savings, including their emergency funds.

Overall, 58 percent of respondents said that the balance of their emergency fund or savings account was greater than their credit card debt, a jump from 52 percent last year.

That's actually a good sign, and perhaps even possible, because "as unemployment declines and household income rises, more households progress on boosting savings, paying down debt or both," Greg McBride, chief financial analyst at Bankrate, says in the survey.

Millennials are leading the pack: 61 percent prioritizing building an emergency savings fund, whereas Baby Boomers and those in Generation X would prefer to pay down debt, according to the survey. Most experts recommend socking away at least three-to-six months' worth of living expenses.

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Not everyone is saving. About 21 percent of respondents owe more on their credit cards than they have set aside for an emergency. In a similar survey, Bankrate found only 39 percent of U.S. adults have enough to cover a $1,000 emergency.

So, "while the results are an improvement," Bankrate notes, they still show "that nearly a third of Americans are just one crisis away from financial hardship."

Millennials are generally on the right track, however. A national survey from Discover found that 81 percent are currently saving in some capacity, compared to 77 percent of Boomers and 74 percent of those in Gen X. And, according to a recent Bank of America survey, one in six millennials now has $100,000 stashed away.

Heather Roche, vice president of deposits at Discover, says, "it is important to remember that consumers should save at all points in their lives. People should start saving early in life and stay consistent in that practice."

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And although paying off your credit card debt in full is a worthy goal, Bankrate points out that it's risky to repay those debts without saving at the same time. It's important to do both: A crisis could leave you in a bind if you don't have the money to handle it; at the same time, too many missed or late credit card payments can have serious impacts on your credit score, like making it more difficult, or expensive, for you to rent an apartment or buy a car.

"Attack both sides of it," says McBride. He suggests you "set up a direct deposit from your paycheck into a dedicated savings account, so the savings happens automatically before you even see it."

Then, "with your net pay, you can focus on cutting expenses and funneling as much as possible toward debt repayment."

Interest-earning accounts can be a good place to stash away an extra income you may have. And, with the money you have dedicated to your credit card bill, eliminate any small, lingering balances and aim to pay your monthly balance in full, on time, every time.

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Suze Orman says this mental shift is the key to saving money