  The transmissivity of a one-dimensional random system that is periodic on
average is studied. It is shown that the transmission coefficient for
frequencies corresponding to a gap in the band structure of the average
periodic system increases with increasing disorder while the disorder is weak
enough. This property is shown to be universal, independent of the type of
fluctuations causing the randomness. In the case of strong disorder the
transmission coefficient for frequencies in allowed bands is found to be a non
monotonic function of the strength of the disorder. An explanation for the
latter behavior is provided.
