  We consider a CP-conserving two-Higgs-doublet type II model with a light
scalar or pseudoscalar neutral Higgs boson ($\h=\hl$ or $\h=\ha$) that has no
$ZZ/WW$ coupling and, thus, cannot be detected in $\epem\to Z\h$
(Higgs-strahlung) or $\nu\anti\nu \h$ (via $WW$ fusion). Despite sum rules
which ensure that the light $\h$ must have significant $t\anti t$ or $b\anti b$
coupling, for a wedge of moderate $\tanb$, that becomes increasingly large as
$\mh$ increases, the $\h$ can also escape discovery in both $b\anti b \h$ and
$t\anti t \h$ production at a $\rts=500-800\gev$ $\epem$ collider (for expected
luminosities). If the other Higgs bosons happen to be too heavy to be produced,
then no Higgs boson would be detected. We demonstrate that, despite such high
masses for the other Higgs bosons, only the low-$\tanb$ portion of the
no-discovery wedges in $[\mh,\tanb]$ parameter space can be excluded due to
failure to fit precision electroweak observables. In the $\tanb\gsim 1$ regions
of the no-discovery wedges, we find that the 2HDM fit to precision electroweak
observables has small $\Delta\chi^2$ relative to the best minimal one-doublet
SM fit.
