  We re-examine a deep {\it Hubble Space Telescope} pencil-beam search for red
dwarfs, stars just massive enough to burn Hydrogen. The authors of this search
(Bahcall, Flynn, Gould \& Kirhakos 1994) found that red dwarfs make up less
than 6\% of the galactic halo. First, we extrapolate this result to include
brown dwarfs, stars not quite massive enough to burn hydrogen; we assume a
$1/{\cal M}$ mass function. Then the total mass of red dwarfs and brown dwarfs
is $\leq$18\% of the halo. This result is consistent with microlensing results
assuming a popular halo model. However, using new stellar models and parallax
observations of low mass, low metallicity stars, we obtain much tighter bounds
on low mass stars. We find the halo red dwarf density to be $<1\%$ of the halo,
while our best estimate of this value is 0.14-0.37\%. Thus our estimate of the
halo mass density of red dwarfs drops to 16-40 times less than the reported
result of Bahcall et al (1994). For a $1/{\cal M}$ mass function, this suggests
a total density of red dwarfs and brown dwarfs of $\sim$0.25-0.67\% of the
halo, \ie , $(0.9-2.5)\times 10^9\msun$ out to 50 kpc. Such a low result would
conflict with microlensing estimates by the \macho\ group (Alcock \etal
1995a,b).
