Cross-conformal prediction is a method for constructing distribution-free predictive sets with valid statistical guarantees. However, the approach can be overly conservative, leading to wide prediction sets. This work explores techniques to enhance the statistical efficiency of cross-conformal prediction by leveraging results on combining dependent p-values. These adjustments preserve coverage guarantees while producing more informative prediction sets. The novelty of this work lies in the application of these methods to a real-world example on housing prices in Milan, demonstrating their practical effectiveness.