As you compare nontraditional CDs, interest rates only tell one part of the story.

From a $5,000 minimum deposit to the requirement to open a personal savings or checking account along with your new CD, many no-penalty and bump-up CDs come with additional strings attached.

While high account balance minimums may intimidate some savers, the savers looking to actively manage their CD portfolios are likely to be able to meet these minimums and give their investment more potential to earn higher interest, Taylor says.

Not all options are restrictions for the saver. Some banks and credit unions offer the ability to contribute money to a CD during the term.

"The ability to add money to your CD is a valuable option," Taylor says.

For example, Taylor says that if a consumer adds money to a two-year, bump-up CD one year before maturity, the additional funds receive the benefit of a higher rate with a shorter term.