Fluorescence spectroscopy combined with parallel factor analysis (PARAFAC) has successfully been applied for the analysis of food and beverages containing numerous autofluorescent compounds. For the decomposition of such data, it is crucial to establish the PARAFAC model complexity. This is not a trivial matter, especially when the sample complexity increases. Diagnostics are available for assisting the choice of the number of PARAFAC components, such as the core consistency. In this short communication, we show that when it comes to real (complex) data, the core consistency is too conservative and other diagnostic tools must be taken into account. We emphasize that it is imperative to inspect the PARAFAC excitation and emission loadings and assess whether these are chemically meaningful.