Can open relationships be moral?

Can it ever be moral to have sex with someone else while in a relationship, assuming that you're honest with everyone involved? If not, why not? If so, what might be some of the pitfalls to be aware of? For example, should the criteria for selecting sexual partners be stricter than if you were single? How should you navigate the tricky territory of opening a previously closed relationship? How might personality differences (especially with respect to sex and intimacy) affect the relationships?