Another common type of alternative CD is the bump-up CD. Most bump-up CDs allow account holders to request a one-time rate increase prior to maturity, but some banks allow multiple requests.

For consumers who invest in bump-up CDs, the goal is to maximize the average yield -- a goal that helps to determine when to request a rate increase from the bank, Taylor says.

"Once you get past the halfway mark, the value of the bump-up option becomes less and less valuable," Taylor says.

Aurora Vidin, deposits product manager at BECU, says that the Washington-based credit union has recently seen an increase in the popularity of its bump-up CDs -- an increase she attributes to the current low-rate environment.

"You need to look at your objectives before you consider taking advantage of the bump-up CD option," Vidin says.

Vidin says reviewing your original savings objectives is crucial before exercising the right to bump up the rate. Bankrate's savings goal calculator can help to determine your current progress and how increased interest rates can accelerate the time to reach your savings goal.