The real-world advantages of Bayesian CP will be discussed more in depth in small-area estimation. This represents a paradigmatic example of how much a Bayesian approach is necessary even in "official" contexts, where the problem of the small sample sizes of individual areas is overcome by the use of indirect information. If "borrowing strength" through Bayesian hierarchical models can endanger the (frequentist) validity, a CP-based approach avoids this eventuality. Starting from the case of unit-level prediction intervals with the standard Gaussian small-area estimation model (Bersson and Hoff; 2024), this talk will then introduce some extensions in the case of proportion data. An application in the context of regional healthcare migration patterns in Italy will be presented. Throughout, emphasis will be placed on the trade-off between small samples and efficiency, as well as computational complexity, discussing practical solutions that make these hybrid methods feasible.