The pressures of giant H II regions in six dwarf irregular galaxies are fou
nd to be a factor of similar to 10 larger than the average pressures of the
corresponding galaxy disks, obtained from the stellar and gaseous column d
ensities. This is unlike the situation for spiral galaxies, where these two
pressures are approximately equal. Either the H II regions in these dwarfs
are all so young that they are still expanding, or there is an unexpected
source of disk self-gravity that increases the background pressure. We cons
ider first whether any additional self-gravity might come from disk dark ma
tter that either is cold H-2 gas in diffuse or self-gravitating clouds with
weak CO emission, or is the same material as the halo dark matter inferred
from rotation curves. The H-2 solution is possible because cold molecular
clouds would be virtually invisible in existing surveys if they were also G
O-weak from the low metal abundances in these galaxies. Cosmological dark m
atter might be possible too because of the relatively large volume fraction
occupied by the disk within the overall galaxy potential. There is a probl
em with both of these solutions, however: the vertical scale heights inferr
ed for irregular galaxies are consistent with the luminous matter alone. Th
e amount of disk dark matter that is required to explain the high H II regi
on pressures would give gas and stellar scale heights that are too small. T
he anomalous pressures in star-forming regions are more likely the result o
f local peaks in the gravitational held that come from large gas concentrat
ions. These peaks also explain the anomalously low average column density t
hresholds for star formation that were found earlier for irregular galaxies
, and they permit the existence of a cool H I phase as the first step towar
d dense molecular cores. The evidence for concentrations of H I in regions
of star formation is summarized; the peak column densities are shown to be
consistent with local pressure equilibrium for the H rr regions. Strongly s
elf-gravitating star-forming regions should also limit the,dispersal of met
als into the intergalactic medium. The third possibility is that all of the
visible H II regions in these dwarf galaxies are strongly overpressured an
d still expanding. The mean time to pressure equilibrium is similar to 15 t
imes their current age, which implies that the observed population is only
7% of the total if they live that long; the rest are presumably too faint t
o see. The expansion model also implies that the volume-filling factor can
reach similar to 100 times the current factor, in which case faint and agin
g H II regions should merge and occupy nearly the entire dwarf galaxy volum
e. This would explain the origin of the giant H I shells seen in these gala
xies as the result of old, expanded H II regions that were formerly driven
by OB associations. The exciting clusters would now be so old and dispersed
that they would not be recognized easily. The shells are still round becau
se of a lack of shear.