  We study the impact of a set of horizontal symmetries on the requirements for
producing the baryon asymmetry of the universe via leptogenesis. We find that
Abelian horizontal symmetries lead to a simple description of the parameters
describing leptogenesis in terms of the small expansion parameter that arises
from spontaneous symmetry breaking. If the family symmetry is made discrete,
then an enhancement in the amount of leptogenesis can result.
