In the last decade a debate in the decision making literature has centered on the question whether decisions can be better described by simple non-compensatory heuristics or by more complex compensatory strategies. We argue that this debate should be led at a higher level of precision Theories about decision strategies are implemented at different levels of description and they often only make verbal, qualitative predictions. This makes it difficult to compare between them and to test them against quantitative process data. A way to make theories comparable and improve the precision of their predictions is to model them within one computational framework. Using the example of the recognition heuristic, we show how simplifying dichotomies such as the one between non-compensatory and compensatory decision strategies can dissolve when using detailed quantitative models.