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ZnSb and Zn₄Sb₃ are interesting as thermoelectric materials because of their low cost and low thermal conductivity. We introduce a model of the lattice thermal conductivity which is independent of fitting parameters and takes the full phonon dispersions into account. The model is found to give thermal conductivities with the correct relative magnitudes and in reasonable quantitative agreement with experiment for a number of semiconductor structures. The thermal conductivities of the zinc antimonides are reviewed and the relatively large effect of nanostructuring on the zinc antimonides is rationalized in terms of the mean free paths of the heat carrying phonons. The very low thermal conductivity of Zn₄Sb₃ is found to be intrinsic to the structure. However, the low-lying optical modes are observed in both Zn-Sb structures and involve both Zn and Sb vibrations, thereby strongly questioning dumbbell rattling. A mechanism for the very low thermal conductivity observed in Zn₄Sb₃ is identified. The large Grüneisen parameter of this compound is traced to the Sb atoms which coordinate only Zn atoms.