However, the rules concerning IRA deductibility are actually similar for 401(k) plans and SIMPLE IRAs; therefore, even if you meet the compensation requirement to contribute to a Traditional IRA, your active-participant status may affect your eligibility to deduct your Traditional IRA contribution. Bear in mind, however, that it is not only your active-participant status that affects your ability to deduct an IRA contribution; your marital status and modified adjusted gross income (MAGI) are also taken into consideration. It is possible, but not guaranteed, that as an active participant, you will be eligible to claim a deduction for your additional Traditional IRA contribution (or part thereof).
For more details, please see Traditional IRA Deductibility Limits.
This question was answered by Denise Appleby