Domain-specific debugging visualizations try to provide a view of a runtime object tailored to a specific domain and highlighting its important properties. The research in this area has focused mainly on the technical aspects of the creation of such views so far. However, we still lack answers to questions such as what properties of objects are considered important for these visualizations, whether all objects have an appropriate domain-specific view, or what clues could help us to construct these views fully automatically. In this paper, we describe an exploratory study where the participants were asked to inspect runtime states of objects displayed in a traditional debugger and draw ideal domain-specific views of these objects on paper. We describe interesting observations and findings obtained during this study and a preliminary taxonomy of these visualizations.