The article deals with the question of what (quantitative) influence Switzerland could potentially obtain as a Community Member State in the EC Council of Ministers. Since the introduction of the Single European Act, and even more after the Treaty on European Union will become effective, qualified majority voting is resorted to increasingly within the Council of Ministers. The article analyzes, based on the Banzhaf Power Index, what influence Switzerland and other potential new EC members would obtain, under the assumption that the present institutional framework will not undergo any fundamental revision by the next enlargement. It is shown that generally, the larger and middle-sized EC member states will lose influence with an enlargement, while the collective influence of the present EFTA members is likely to be between 19 and 26 percent of total voting power. Depending on the enlargement scenario worked with, the quantitative influence of Switzerland would approximately lie between 3 and 5 percent of total voting power.