While it is well known that trade policy can be used to counter foreign firm market power, it suffers from a lack of robustness over what form it should take. If the import demand function has a certain curvature then a tariff will improve importer welfare while an import subsidy will lower it. However, the opposite holds if the import demand function has a different shape. Picking the right option is made even more difficult as there is little hope of confidently identifying the curvature of import demand. This paper demonstrates that moving beyond the either/or dichotomy and using a combination of an ad valorem tariff and a specific import subsidy can completely offset a foreign firm’s market power. This policy is not subject to the information constraints that undermine the single instrument choice, making it more robust. Combining it with a simple fiscal neutrality constraint delivers an efficient outcome, which is also robust to; country size; whether the market power is in the hands of a foreign exporter (monopoly) or importer (monopsony); and, more generally, the nature of conduct when more than one foreign firm has market power (oligopoly/oligopsony).