Both of those actions will sink your score.
Here's how it works: When you apply for a new credit card, a lender will pull your credit report and score. This is called a "hard" credit inquiry, and it'll hurt your score. (It doesn't hurt your score, by the way, when you pull your own credit report. It also doesn't hurt when an employer pulls your credit report or when a lender pulls your credit report for marketing purposes. Those are called "soft" inquiries.)
If you have several hard credit inquiries in a short amount of time, the damage to your credit score increases dramatically, says Anthony Sprauve, spokesman for myFICO.com, the consumer education division of FICO.
"Our data shows that someone opening multiple credit accounts in a short period of time is at a higher risk for default," he says.
It's unclear how much a hard inquiry -- or several of them -- will hurt your credit score. It depends on the cardholder, Sprauve says. Typically, the higher your credit score, the harder it gets hit by any credit transgression, he says. Consumers with low credit scores will find that a hard inquiry doesn't hurt their already low credit score by the same amount.
The damage from these hard inquiries will lessen over time as long as you manage the new credit responsibly. That means paying your bills on time and keeping the balances below 20 percent of the total available credit, Sprauve says.
New credit accounts also hurt your FICO credit score by lowering the average length of your overall credit history. The average age of all your accounts, the age of individual accounts and the length of time since you used certain accounts all contribute 15 percent to your FICO credit score. As the accounts age, and if you manage them responsibly, those new accounts will eventually boost your credit score.
So be careful with those credit card offers. While it's attractive to sign up for rewards credit cards, especially since many of them offer cash bonuses for new cardholders, do so with prudence and only when you need new credit.
"In addition to paying bills on time and keeping revolving credit balances low," Sprauve says, "the third most important thing a person can do to improve their credit is only open new accounts when necessary."
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To ask a question of the Credit Card Adviser, go to the "Ask the Experts" page and select "Credit Cards." Read more columns by the Credit Card Adviser. Follow Janna Herron on Twitter.