  Models of leptogenesis are constrained by the low reheat temperature at the
end of reheating associated with the gravitino bound. However a detailed view
of reheating, in which the maximum temperature during reheating, $\Tmax$, can
be orders of magnitude higher than the reheat temperature, allows for the
production of heavy Majorana neutrinos needed for leptogenesis. But then one
must also consider the possibility of enhanced gravitino production in such
scenarios. In this article we consider gravitino production during reheating,
its dependence on $\Tmax$, and its relevance for leptogenesis. Earlier
analytical studies of the gravitino abundance have only considered gravitino
production in the post-reheating radiation dominated era. We find that the
gravitino abundance generated during reheating is comparable to that generated
after reheating. This lowers the upper bound on the reheat temperature by a
factor of 4/3.
