If you or your spouse were covered by a retirement plan in 2016 (even if for one day), and made more than the limit, you won't be able to contribute to a deductible IRA.
You can still
contribute to a non-deductible IRA, then convert to a Roth IRA (back-door
Roth).
Nondeductible IRAs are
available to anyone with earned income regardless of how much they make,
although few people use them since they don't offer any upfront tax benefit.
This will give you
tax-deferred growth in the nondeductible IRA, and if you convert to a Roth IRA,
tax-free treatment later.
https://www.irs.gov/retirement-plans/plan-participant-employee/2016-ira-contribution-and-deduction-l...
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