Various hints for anisotropies in the distribution of arrival directions of ultra-high-energy cosmic rays (UHECRs) have been reported. Still, our poor knowledge about intergalactic and Galactic magnetic fields and about the UHECR mass composition makes it non-trivial to interpret such results in terms of possible models of UHECR sources. In this work, we apply the same analyses that have been performed on the Pierre Auger Observatory and the Telescope Array UHECR data to a variety of Monte Carlo simulations generated according to many different combinations of hypotheses about the sources, composition and magnetic deflections of UHECRs. We find that only some of these models can yield results similar to those obtained with the real data.