We derive a new formula for the optimal uniform tariff in a small-country, heterogeneous-firm model with roundabout production and a nontraded good. Tariffs are applied on imported intermediate inputs. First-best policy requires that markups on domestic intermediate inputs are offset by subsidies. In a second-best setting where such subsidies are not used, roundabout production and the monopoly distortion in the traded sector create strong incentives to lower the optimal tariff on imported inputs. In a quantitative version of our two-sector small open economy, we find that the optimal tariff is lowered under nearly all parameter values considered, and can be negative.