  We prove that any smooth complex projective variety with generic vanishing
index bigger or equal than 2 has birational bicanonical map. Therefore, if X is
a smooth complex projective variety X with maximal Albanese dimension and
non-birational bicanonical map, then the Albanese image of X is fibered by
subvarieties of codimension at most 1 of an abelian subvariety of Alb X.
