Measurements have been made at liquid helium temperatures of the thermal conductivity of nine specimens of copper containing germanium, aluminum, gallium, or indium impurities. The residual resistivities varied from 0.3 to 12.5 μΩ-cm. The results for the lattice conductivity Kg of all specimens lie close to a single curve on a graph of Kgρ0T against Tρ0. Numerical calculations of the lattice conductivity have been made, using Pippard's theory of the dependence of the electron-phonon interaction on the electronic mean free path. The theory agrees well with our results and those of others if it is assumed that the longitudinal and transverse modes interact with the electrons nearly independently of each other. In the purer specimens the lattice conductivity is dominated by the transverse modes. The change in lattice conductivity between different specimens is seen to be the result of the change in the electron-phonon interaction without the necessity of assuming a large dislocation resistance. It is shown that dislocations do not cause a significant thermal resistance in annealed specimens. © 1962 The American Physical Society.