  We demonstrate that Abelian family symmetries allow one to enforce texture
zeros in arbitrary entries of the fermion mass matrices. Placing zeros in any
number of elements of all occurring mass matrices can be done with two
alternative methods; one of them utilizes the group Z_n with n sufficiently
high. Concentrating on the lepton sector and on neutrino masses, we discuss the
methods in the case of seesaw models and scalar triplet models. As an
illustration, we present an example for each type of model.
