  ``Natural'' inflationary theories are a class of models in which inflation is
driven by a pseudo-Nambu-Goldstone boson. In this paper we consider two models,
one old and one new, in which the potential for inflation is generated by loop
effects from a fermion sector which explicitly breaks a global $U(1)$ symmetry.
In both models, we retrieve the ``standard'' natural inflation potential,
$V\left(\theta\right) = \Lambda^4\left[1 + \cos\left(\theta /
\mu\right)\right]$, as a limiting case of the exact one-loop potential, but we
carry out a general analysis of the models including the limiting case.
Constraints from the COBE DMR observation and from theoretical consistency are
used to limit the parameters of the models, and successful inflation occurs
without the necessity of fine-tuning the parameters.
