We propose a new three-step model-selection framework for size distributions in empirical data. It generalizes a recent frequentist plausibility-of-fit analysis (Step 1) and combines it with a relative ranking based on the Bayesian Akaike Information Criterion (Step 2). We enhance these statistical criteria with the additional criterion of microfoundation (Step 3) which is to select the size distribution that comes with a dynamic micro model of size dynamics. A numerical performance test of Step 1 shows that our generalization is able to correctly rule out the distribution hypotheses unjustified by the data at hand. We then illustrate our approach, and demonstrate its usefulness, with a sample of commercial cattle farms in Namibia. In conclusion, the framework proposed here has the potential to reconcile the ongoing debate about size distribution models in empirical data, the two most prominent of which are the Pareto and the lognormal distribution.