We reply to each of the issues raised by Schwartz in a commentary on our article on a comparison of value taxonomies. We discuss two approaches, mentioned in that commentary, the lexical approach and the theory-driven approach, especially with respect to their capacities in covering the domain of values and with respect to the representation of important values in a useful structure. We refute the critique by Schwartz that the lexical approach is superfluous, because his theory “toward universals in values” would already cover all values, and that their mutual relationships are relevant to individuals around the globe. We explain the necessity and strength of the lexical approach in taxonomizing the value domain, both within and across languages. Furthermore, we argue that principal components analysis (PCA) and simultaneous component analysis (SCA) are most adequate in arriving at a satisfactory structuring of the great many values in terms of both underlying constructs and their facets. We point to a misrepresentation in Schwartz’s circular model, and we review some misunderstandings on the side of Schwartz with respect to our results in comparison with those proceeding from his circular model.