Research on moral judgment has shown that the order in which dilemmas are presented to subjects often has a strong influence on their judgment. However, the psychological mechanisms underlying order effects are still opaque. In this paper we aimed to isolate the features that a scenario must exhibit in order to influence judgment of subsequent scenarios. For this enterprise, we identified several features from a scenario known to cause order effects, and tested which of these features are necessary to influence subsequent scenarios. Although we still do not have a full understanding of what causes order effects, we made significant progress towards this aim. In five experiments we ruled out some promising explanations such as order effects being driven by an emotional activation linked to the first scenario. Instead, we found order effects to depend on whether the scenario being influenced and its preceding scenario share rather subtle structural similarities.