We present a three-nation model, where two of the nations are members of a Customs Union (CU) and maintain a common external tariff (CET) on the third (non-member) nation. The producing lobby is assumed to be union-wide and lobbies both governments to influence the CET. The CET is determined jointly by the CU. We follow the political support function approach, where the CU seeks to maximize a weighted sum of the constituents’ payoff functions, the weights reflecting the influence of the respective governments in the CU. A central finding of this paper is that the CET rises monotonically with the degree of asymmetry in the weights if the two countries are equally susceptible to lobbying. If the weights are the same, but the respective governments are asymmetric in their susceptibilities to lobbying, the CET also rises monotonically with this asymmetry. However, an increase in one type of asymmetry, in the presence of the other type of asymmetry, may reduce the CET.