Abstract Compared with d-band metals of the same valency, La shows a similar anomalous thermal behaviour to that observed for Ce (e.g. low melting point, low Debye frequency). We show that the soft phonons in these systems are induced by the ⨍-band, which is known to intersect the Fermi level in α-Ce and to lie slightly above it in La. We therefore calculate the RPA dielectric constant for a simple two-band model of d-and ⨍-electrons and show that it is enhanced due to the high density of states of the ⨍-band near the Fermi energy. The phonon frequencies, renormalized by this enhanced dielectric constant, are thus lowered.