We report Raman measurements of the superionic conductor CuI in all three crystallographic phases. There is considerable temperature variation of the spectra in the zinc-blende phase, below 369°C. The temperature variation is much less in the hexagonal phase (369-407°C) and in the ± phase above 407°C. However, abrupt changes in the spectra are observed at the phase transitions. Using a harmonic lattice-dynamic model, with the four Cu ions randomly positioned among eight proposed sites in the ±- phase unit cell, we have calculated the density of states, infrared conductivity, and Raman scattering. For this model we take the force constants from those we find in the zinc-blende phase and make no further adjustments. The model explains the main features of the experimental results, as we have also found in AgI which has a different crystal structure. Thus, we conclude that the phonon spectra (above 10 cm-1) in these simple superionic conductors can be understood in terms of ordinary lattice dynamics when the disorder in the structures is taken into account. Some of the more complex assumptions, contained in earlier models, are not required. © 1979 The American Physical Society.