Standard preference models in consumer research assume that people weigh and add all attributes of the available options to derive a decision, while there is growing evidence for the use of simplifying heuristics. Recently, a greedoid algorithm has been developed (Yee, Dahan, Hauser & Orlin, 2007; Kohli & Jedidi, 2007) to model lexicographic heuristics from preference data. We compare predictive accuracies of the greedoid approach and standard conjoint analysis in an online study with a rating and a ranking task. The lexicographic model derived from the greedoid algorithm was better at predicting ranking compared to rating data, but overall, it achieved lower predictive accuracy for hold-out data than the compensatory model estimated by conjoint analysis. However, a considerable minority of participants was better predicted by lexicographic strategies. We conclude that the new algorithm will not replace standard tools for analyzing preferences, but can boost the study of situational and individual differences in preferential choice processes.