Phonon calculations on CuI were performed with DFPT and ABINIT using PBEsol+SOC and a 9 × 9 × 9 q-mesh following the methodology used by Petretto et al. The structures were relaxed until all the forces on the atoms and the stresses are respectively below 10 -6 Ha/Bohr and 10 -4 Ha/Bohr 3 using a plane-wave cut-off of 46 Ha. Defect calculations were performed with VASP on a 64 atom supercell and with a Γ-centred 2 × 2×2 k-point mesh. Each defect was fully relaxed using the PBE0 functional, followed by a spin-orbit coupling single-shot calculation to obtain accurate energies. This goes beyond the GGA relaxation plus hybrid single-shot calculations of Graužinyt ė et al., fully capturing lattice distortions caused by charge localisation that would otherwise be missed with a semi-local exchange-correlation functional. The potential energy surface was explored using the ShakeNBreak method. Defect formation energies were obtained in the usual fashion, within the Lany-Zunger formalism: Δ𝐸 (𝐷,𝑞)