The results of a detailed numerical study of the optical bandtail in a
1D randomly-perturbed periodic system are reported. It is found that
the width of the optical bandtail grows proportionally to the magnitud
e of the random perturbations. and the states in the bandtail regime,
which are tightly localized, are separated from the more extended stat
es in the pass band by a quasi mobility edge. Frequency dependence of
the localization length and its relation to the distribution of the ra
ndom perturbations are also examined.