This study focused on misspecifications in composing parcels to represent a latent construct. Two measurement design factors, item reliability and intercorrelations among parcels, defined 12 true unidimensional parcel models. Deviations from the true model were examined via a 2-facet measurement model in which items and parcels represented the 2 facets. Unidimensionality was examined using a set of criteria developed for the 2-facet measurement model. Many misspecified parcel models produced admissible factor loadings despite poor overall fit and unacceptable residual covariances. The factor loadings alone may not be sufficient for evaluating latent factor representation. The findings suggest that parcels' unidimensionality should be analyzed before the measurement model to which they belong is entered into a comprehensive structural model. The 2-facet measurement model provides a relevant assessment of unidimensionality of the parcel compositions.