A duty drawback is an export subsidy determined as a percentage of the tariffs paid on the imported inputs used in its production. This paper examines the revenue-constrained optimal tariff structure in a small open economy including a duty drawback as a trade policy tool. This paper has two main aims. First, we show that the revenue-constrained optimal combination of tariff and duty drawback for a given revenue level is not unique. Second, we show that if the optimal import tariff rates are all positive when the duty drawback rate is zero, then the optimal import tariff rates are always positive when the duty drawback is positive.