Lattice thermal conductivity is the part of the thermal conductivity of a solid that is carried by lattice vibrations rather than by electrons, and in semiconductors and insulators it is usually the whole of it. It is the quantity that has to be minimised in a thermoelectric, because the figure of merit improves as the thermal conductivity falls while the electronic transport is left intact, and the standard strategy is to shorten the phonon mean free path by alloying, by introducing heavy or rattling atoms, or by nanostructuring, without degrading carrier mobility to the same extent. Some crystal structures are intrinsically poor conductors because of anharmonic bonding or a complex unit cell, and identifying them has become a screening exercise in its own right ^[1]. In a two-phase alloy the measured value is not a simple average of the constituents, since the interfaces scatter phonons as well, so a practical estimate needs a model of that extra resistance ^[2]. First-principles calculations of the lattice dynamics now predict the conductivity from the interatomic force constants alone ^[3]. They rank candidate compounds before they are made ^[4]. Compounds with a layered or a loosely bonded structure reach the lowest values, in some cases below one watt per metre per kelvin ^[5].