Abstract: This paper compares strategic barriers to the resolution of conflict - those that may arise because rational self-interested actors try to maximize individual returns - in two party and multi-party negotiations. It suggests that the Pareto-criterion may not provide an appropriate standard to evaluate efficiency in multiparty bargaining because a requirement of unanimity may create potential holdout problems that pose severe strategic barriers. While a variety of procedural rules may permit decision-making without unanimity, the paper briefly explores the application of an unusual procedural rule - the "sufficient consensus" standard - that was employed in the multiparty "constitutional" negotiations in South Africa and in Northern Ireland.