Our analysis provides some clear guidance for optimising the thermal transport in the group IV-VI chalcogenides. If low κ κ κ latt is desired, as for thermoelectric applications, a structure with a large and/or low-symmetry unit cell in which the tetrel atoms are constrained to a locally-symmetric environment should be sought. While seemingly contradictory, these requirements appear to be met in the Cmcm phase, which is accessible to some of the chalcogenides at high temperature and/or under pressure. Alternatively, it might be possible to use alloying or doping to stabilise the chalcogenide in a rocksalt or R3m phase while reducing the group velocities. If, on the other hand, high κ κ κ latt is required, as might be the case e.g. for power electronics, a relatively simple structure in which the tetrel atom can adopt a low-coordinate geometry with an active lone pair should be sought. We note also that while we have focussed on chalcogenides in this work, it is likely that the same considerations would apply to the analogous group VI oxides.