As the economy begins to pick up and as the Federal Reserve hints at a possible interest rate rise, investors are following their historical pattern and losing interest in classic certificates of deposit.

Similarly, banks are responding by offering a growing number of alternative rising-rate CD products to keep investors interested.

Bankrate.com, in a 2011 rising-rate survey, found a surprising range of opening interest rates among all three categories: liquid CDs, step-up CDs and bump-up CDs.

"The terms in all three categories vary widely, as do the interest rates," said Greg McBride, a senior financial analyst at Bankrate.com. "That means that the customer has to really shop around for the best deal." The results were released Monday.

He said people should also compare the whole class of alternative CDs with a higher-yielding savings account or with traditional CDs, because rising-rate products generally offer their provisions at a cost in terms of interest. McBride says there is no real correlation between how high interest rates are and how restrictive a product's terms are, making shopping all the more important.

For example, consider the case of liquid CDs, which allow the holder to withdraw money before term without penalty. Offerings range from the extremely restrictive, such as Colonial Savings of Dallas' 36-month CD, which pays 1.67%, but allows only one penalty-free withdrawal of up to 50%, to relatively liberal Suncoast Federal Credit Union, which pays 1.3% on its 36-month CD, but allows withdrawals or a closeout, penalty free. Meanwhile BB&T Bank in Washington, which offers a liquid 36-month CD that permits up to four penalty-free withdrawals a year, pays only 0.75% interest, and withdrawals must be for tuition or to buy a home.

Similarly, the 24-month bump-up CD products show interest running from Sovereign Bank's 0.15% starting rate to Ent Federal Credit Union's 1.36% rate, yet both offer the same one-time opportunity to bump up the rate.

In the step-up category, the range of offerings is widest, running from PNC Bank's 36-month CD that kicks off at a 0.25% annual yield rising at six-month intervals to 1.4% for a yield to maturity of 0.82%, to American Airlines Federal Credit Union's 36-month CD that starts at 1.76%, rising in two steps to 2.78%, for a yield to maturity of 2.27%.

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