Efficient phosphor performance, meaning a high photoluminescence quantum yield (Φ), requires the Ce3+ ion to be hosted in a rigid crystal structure. This is particularly important when the phosphor is operated at slightly elevated temperatures, as is becoming conventional in high brightness, phosphor-converted white solid-state light-emitting diodes. We find the Debye temperature (ΘD) of the undoped host crystal structure, which is readily calculated using ab initio methods within the quasi-harmonic approximation, is a useful proxy for structural rigidity. ΘD is found here to correlate well with the experimentally measured Φ for a number of Ce3+ phosphors. In addition to being rigid, the host lattice must possess a large enough band gap (Eg) that the Ce3+ 4f to 5d transition can occur without interference from a host energy channel. As a sorting diagram for efficient hosts with high Φ, we propose using Eg of the host, also readily calculated with high reliability using hybrid functionals, as one of the ax...