This is one of the problems with our tax code. Opinions about what's allowed can change. Recent tax changes allowed those over the income limits to contribute to a Roth IRA through a backdoor method. In this approach, you can make a non-deductible contribution to a traditional and then immediately convert it into their Roth. This Five Cent Nickel post
has a good review of current discussion of the possibility that these contributions could be disallowed.