First of all, make sure your credit score is high enough to qualify. As a rule, airline co-branded credit cards are for people with good or excellent credit. Those whose credit is close to good credit, may also qualify for such card. Then, if your primary goal is credit building only, the Icelandair card is one of good options. But if you want to earn some points, it may not be as good. The card’s rewards program is not one of the rewarding, and if you are planning to carry a balance, your points may be eaten by interest. When applying for a rewards credit card, it is recommended to pay off the card balance in full each month to get the most out of the rewards.