Two methods are used to simulate charge transport in CuI: an iterative Boltzmann transport equation (IBTE) solution to calculate phonon-limited mobilities using the ABINIT code; and a phenomenological model (AMSET) that calculates scattering rates for acoustic deformation potential (ADP), piezoelectric (PIE), ionised impurity (IMP) and polar optical phonon (POP) scattering, utilising low-cost inputs from first-principles calculations using the VASP code. While IBTE provides a high-quality representation of transport properties, AMSET complements the analysis by evaluating the effects of impurities but also by providing an additional analysis of the phonon scattering mechanisms by decoupling the different contributions. AMSET also offers the advantage of using hybrid functionals, which are difficult to employ in fully first-principles IBTE calculations due to the computational cost and absence of implementations able to compute electron-phonon (e-ph) quantities within density functional perturbation theory (DFPT). The methodology for each approach is outlined in the Supplementary Information.