Five Tips for Nabbing the Best Bank Rates

McClary also suggests using arguments that are compelling from a bank's point of view. Noting more attractive offers from the competition or the potential for more business down the line can move the dial in your favor.

There are two tactics McClary warns against: Stating the length of time you've been a customer or being argumentative.

"Don't negotiate out of anger -- that will derail everything," he says. "Pour on the honey."

5. Don't be afraid to walk out or switch banks.

Negotiating can be tough, especially if it's your first time.

"It's like giving a speech or playing a sport," says Ryan. "The more you practice, the more comfortable you are doing it."

Still, even beginners should never be pressured into a deal they're uncomfortable with. Don't be afraid to go home and sleep on it, or make good on a threat to sign with the competition -- even if that means leaving a bank you've been loyal to for years.

"People certainly shouldn't feel pressured, because they're in control," says Ryan. "Don't be afraid to say, 'I'm going to look around a little more' or 'I'm going to walk away.'"