This paper proposes a methodology to identify revenue-neutral directions for poverty-alleviating tax reforms. The search for such poverty-reducing tax reforms is done “robustly” over broad classes of poverty measures and poverty lines. The methodology, which is illustrated using data from Tunisia, is of significant policy interest given the widespread use of commodity subsidization and taxation in developing and developed countries alike. The results suggest that Tunisian poverty could be decreased robustly by following reform directions that are often at odds with frequently-heard views. They also highlight the importance of stating clearly under which set of ethical criteria the desirability of potential indirect tax reforms is assessed.