Investigates band-tail states in a system of polar oscillators that have disordered short-range force constants. In the absence of disorder, the frequencies of the transverse and longitudinal modes are separated by Lyddane-Sachs-Teller splitting. The states in the band tail appear to be formed as a result of large fluctuations in the short-range force constants on a small number of atoms. This contrasts with band-tail states in disordered electronic systems which arise because of negative fluctuations in the potential over a large number of atoms.