An exact calculation of the acoustic‐phonon‐assisted jump rate has been carried out. It is found that although the Miller and Abrahams jump‐rate expression constitutes an adequate approximation to the jump rate in the highly restrictive situation to which they have applied it (impurity conduction between very shallow impurity states at helium temperatures), their expression does not generally provide even a qualitatively correct representation of the jump rate. Specifically, multiphonon transitions will, in many instances, provide the dominant contribution to the jump rate even as the temperature approaches absolute zero. The multiphonon jump rate will manifest a non‐activated temperature‐dependence, resembling aexp[ −(T0/T)1/4]behavior, between helium temperatures and some fraction of the Debye temperature. In fact, the present study suggests that the non‐activated temperature dependence of the electrical conductivity, which is observed in a number of non‐ crystalline solids in this temperature range, may arise, in the main, from the jump‐rate itself rather than from the percolation aspects of hopping conduction in disordered materials.