  Many experts believe that the z ~ 3 HeII Ly-alpha forest will suffer from the
same saturation issues as the z ~ 6 HI Ly-alpha forest and, therefore, will not
be a sensitive probe of HeII reionization. However, there are several factors
that make HeII Ly-alpha absorption more sensitive than HI Ly-alpha. We show
that observations of HeII Ly-alpha and Ly-beta Gunn-Peterson troughs can
provide a relatively model-independent constraint on the volume-averaged HeII
fraction of x_HeII >~ 0.1. This bound derives from first using the most
underdense regions in the HeII forest to constrain the local HeII fraction and,
then, assuming photoionization equilibrium with the maximum allowed
photoionization rate to calculate the ionization state of nearby gas. It is
possible to evade this constraint by a factor of ~2, but only if the HeII were
reionized recently. We argue that HeII Ly-alpha Gunn-Peterson troughs observed
in the spectra of Q0302-003 and HE2347-4342 signify the presence of >~ 10
comoving Mpc patches in which x_HeII > 0.03. This is a factor of 20 improvement
over previous constraints from these spectra and 100 times stronger than the
tightest constraint on the HI volume-filling fraction from the z>6 HI Lyman
forest.
