A characteristic of many bargaining situations is that the negotiators represents the interests of a set of parties (trade unions, political parties, etc.) with composite interests, whose bargaining behaviour is regulated by some collective decision mechanism. In this paper we provide a natural model of such circumstances, and show how different preference aggregation procedures within the composite player affect the bargaining outcome. In particular we find that unanimity procedures lead to 'more aggressive' behaviour than majority procedures, and that procedures which introduce minimum safeguards for the members of an alliance may result in agreements that are worse than without those safeguards.