Within the field of project management, research in the subject of conflict analysis and resolution has received considerable attention. This paper presents the application of cognitive analysis, based on the workings of “human judgment theorists,” to the resolution of representative conflict situations. The employed conflict-resolution approach presents cognitive differences between parties as a primary source of conflict. However, it also presents feedback that provides analysis of each individual's judgment and comparisons with his or her counterpart's judgment. This feedback, termed “cognitive feedback,” is used as a way to give insight to people in conflict, providing them an opportunity to resolve their conflicts acceptably. The objective of this paper is to establish a systematic methodology for analyzing and resolving conflict. An actual case study of conflict resolution between union and management personnel at a petrochemical plant in Kuwait is used to illustrate the methodology. Both self-understanding and the understanding of one's counterpart were found to be generally poor before receiving cognitive feedback. The use of cognitive feedback for both groups proved feasible and helped reduce conflict.