An important qualitative conclusion is that large average mass and/or weak chemical bonding, which are often taken to be indicators of low lattice thermal conductivity, are secondary to the complexity of the structure. On this point we note that, with the exception of the two R3m structures, the chalcogenide phases with larger n a also have lower-symmetry structures, so we cannot easily decouple these in our definition of "structural complexity". However, our previous work on the Si clathrates 41 strongly suggests that the n a rather than the crystal (spacegroup) symmetry is likely to be the key descriptor. In this context, calculations on the π-cubic structure reported as a synthetically-accessible phase of SnS and SnSe 67,68 will be illuminating, since the π phase has a high-symmetry cubic P2 1 3 spacegroup but a complex structure with n a = 64 atoms in the primitive cell. Another interesting observation from our analysis is the imaginary modes in Cmcm SnSe producing a steep dispersion and larger ν ν ν λ compared to the Pnma phase. The impact of anharmonic renormalisation and potential phonon softening at elevated temperature on this behaviour requires further investigation.