Many attempts to understand the success of simple decision heuristics have examined heuristics as an approximation to a linear decision rule. This research has identified three environmental structures that aid heuristics: dominance, cumulative dominance, and noncompensatoriness. Here, we further develop these ideas and examine their empirical relevance in 51 natural environments. We find that all three structures are prevalent, making it possible for some simple rules to reach the accuracy levels of the linear decision rule using less information.