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Combining items into parcels in confirmatory factor analysis (CFA) can improve model estimation and fit. Because adequate model fit is imperative for CFA tests of measurement invariance, parcels have frequently been used. However, the use of parcels as indicators in a CFA model can have serious detrimental effects on tests of measurement invariance. Using simulated data with a known lack of invariance, the authors illustrate how models using parcels as indicator variables erroneously indicate that measurement invariance exists much more often than do models using items as indicators. Moreover, item-by-item tests of measurement invariance were often more informative than were tests of the entire parameter matrices.