Abstract Variational arguments are employed to present the first explicit derivation of the behavior of band tail states and localization length over most of the tail region of a random alloy. Exponential tails are shown to exist near the mobility edges, in conformity with the observation in disordered systems. The character of the states forming the band tails is discussed and, for random alloys, the localization length is shown to exhibit a minimum as a function of energy between band edge and mobility edge.