The assessment of the number of dimensions and the dimensionality structure of questionnaire data is important in scale evaluation. In this study, the authors evaluate two dimensionality assessment procedures in the context of Mokken scale analysis (MSA), using a so-called fixed lowerbound. The comparative simulation study, covering various theoretically and empirically relevant conditions, indicates that the MSA procedures may result in scales that are inconsistent with the dimensionality of the data set at hand. That is, a single Mokken scale can be multidimensional, and two Mokken scales can pertain to a single dimension. In an illustrative evaluation, MSA using a range of lowerbounds, rather than a fixed lowerbound, was shown to have some benefits, but not to solve all limitations. The results of this study imply that MSA is perfectly suitable to create Mokken scales. However, MSA appears of limited value as a dimensionality assessment method. (Contains 3 tables and 4 figures.)