This paper analyzes the a priori influence of the European Parliament (EP) and the Council of Ministers (CM) on legislation of the European Union adopted under its codecision procedure. In contrast to studies which use conventional power indices, both institutions are assumed to act strategically. Predicted bargaining outcomes of the crucial Conciliation stage of codecision are shown to be strongly biased towards the legislative status quo. Making symmetric preference assumptions for members of CM and EP, CM is on average much more conservative because of its internal qualified majority rule. This makes CM by an order of magnitude more influential than EP, in contrast to a seeming formal parity between the two ?co-legislators?.