Hierarchical classes (HICLAS) models for multi-way multi-mode data constitute a unique family of classification models in that (a) they simultaneously induce a hierarchical classification (of the elements) of each mode and (b) they link the hierarchical classifications together by an association relation that yields a predicted (or reconstructed) value for each cell in the data array. For the case of three-way three-mode binary data, the most prominent HICLAS models include INDCLAS and Tucker3-HICLAS. In this paper, we compare the latter two models, introducing the underlying theory of both in substantive terms and showing how a Tucker3-HICLAS analysis may result in a simpler model than that yielded by INDCLAS, although the former is mathematically more complex than the latter (which it includes as a special case). We illustrate by two applications: a study on anger responses in frustrating situations and a case-study on emotions in interpersonal relations.