  The accepted explanation of the observed dichotomy of two orders of magnitude
between in situ measurements of electron density in HII regions, derived from
emission line ratios, and average measurements based on integrated emission
measure, is the inhomogeneity of the ionized medium. This is expressed as a
"filling factor", the volume ratio of dense to tenuous gas, measured with
values of order 10^-3. Implicit in the filling factor model as normally used,
is the assumption that the clumps of dense gas are optically thin to ionizing
radiation. Here we explore implications of assuming the contrary: that the
clumps are optically thick. A first consequence is the presence within HII
regions of a major fraction of neutral hydrogen. We estimate the mean H^o/H^+
ratio for a population of HII regions in the spiral galaxy NGC 1530 to be the
order of 10, and support this inference using dynamical arguments. The
optically thick clumpy models allow a significant fraction of the photons
generated by the ionizing stars to escape from their HII region. We show, by
comparing model predictions with observations, that these models give an
account at least as good as, and probably better than that of conventional
models, of the radial surface brightness distribution and of selected spectral
line diagnostics for physical conditions within HII regions. These models
explain how an HII region can appear, from its line ratios, to be ionization
bounded, yet permit a major fraction of its ionizing photons to escape.
