  We study the impact for leptogenesis of new U(1) gauge bosons coupled to the
heavy Majorana neutrinos. They can significantly enhance the efficiency of
thermal scenarios in the weak washout regime as long as the Z' masses are not
much larger than the reheating temperature ($M_{Z'}<10 T_{rh}$), with the
highest efficiencies obtained for Z' bosons considerably heavier than the heavy
neutrinos ($M_{Z'} > 100 M_1$). We show how the allowed region of the parameter
space is modified in the presence of a Z' and we also obtain the minimum
reheating temperature that is required for these models to be successful.
