As you can see from the many answers, it should not be a problem to purchase in one name only. Beware that there could be an issue when you get ready to sell, however. I don't know about the laws in Arizona, but in some states, like Missouri, your spouse has rights to the property even if his name is not on the deed. In community property states like this, your spouse owns 50% of the property and has to sign either a "Quit Claim Deed" or a "Waiver of Marital Rights" for you to sell it. Protect yourself by knowing the laws of your state before you make a costly mistake. If you are not certain about how to proceed, consult an attorney. Good luck to you!