The best deal on a certificate of deposit still isn't thrilling. But savers are starting to see more promotions in the 1.25 to 2 percent range that might be worth a second look.

And better yet, rates could continue to improve into 2018, as competition heats up between banks.

The average yield for a one-year CD across the country is 0.41 percent — up from 0.31 percent a year ago, according to Bankrate.com. The average yield on a five-year CD is 0.99 percent — up from 0.82 percent a year ago.

Today's CD rates aren't anywhere close to the 5 percent that savers could snag in late 2007, just as the U.S. economy tanked and took down rates with it.

As a result, retirees who typically turn to CDs to offer some security for their nest eggs won't find too much relief ahead.

Even so, it is worthwhile to note that savers who shop around for rates are being rewarded as more banks roll out limited offers.

Some offers require sizable deposits. But plenty of other offers only require minimum deposits that range from $500 to $5,000.

"You often can get the top rate or close to the top rate with a deposit as low as $500, and in some cases, the minimum deposit can even be lower," said Ken Tumin, founder and editor of DepositAccounts.com.

Typically, much lower CD rates will be offered at some large banks if there are no special deals. Tumin said the average CD rates at large bank are 30 to 40 percent lower than at small and medium-size banks

Chase's website, for example, last week indicated that a 12-month CD has a yield of 0.02 percent for deposits less than $100,000.

Bank of America offers a 0.07 percent yield on a 12-month CD with a minimum opening balance of $10,000.

Consumers should look at internet-only banks, community banks and credit unions, which can have CD rates that are well above the averages.

The Capital One 360 one-year online CD has an APY of 1.65 percent. Capital One 360 has a five-year online CD with a yield of 2.45 percent.

Ally Bank has a no-penalty 11-month CD that has a yield of 1.5 percent with deposits of $25,000 or higher. The yield is 1 percent on that 11-month CD for deposits of less than $5,000. No penalties are charged for withdrawing the money before the CD matures after the first six days of putting money into the CD.

While CD rates are likely to gradually increase, few market watchers expect a dramatic increase anytime soon.

Susan Tompor is the personal finance columnist for the Detroit Free Press.