Abstract: Conflicts over important moral differences can divide communities and trap people in destructive spirals of enmity that become intractable. But these conflicts can also be managed constructively. Two laboratory studies investigating the underlying social–psychological dynamics of more tractable versus intractable moral conflicts are presented, which tested a core proposition derived from a dynamical systems theory of intractable conflict. It portrays more intractable conflicts as those, which have lost the complexity inherent to more constructive social relations and have collapsed into overly simplified, closed patterns of thinking, feeling, and acting that resist change. Employing our Difficult Conversations Lab paradigm in which participants engage in genuine discussions over moral differences, we found that higher levels of cognitive, emotional, and behavioral complexity were associated with more tractable conversations. Whereas in a pilot study we examined conflicts that naturally became more/less intractable, in our main experiment, high versus low levels of cognitive complexity were induced.