  We have combined deep starcount data with Galaxy model predictions to
investigate how effectively such measurements probe the faint end of the halo
luminosity function. We have tested a number of star/galaxy classification
techniques using images taken in 0.5 arcsecond seeing with LRIS on the Keck
telescope, and we find that different combinations of these techniques can
produce variations of 10 \% in the inferred starcounts at R=22.5 and 30 \% at
R=24.5 magnitudes. The decreasing average angular size of galaxies with fainter
magnitude effectively limits ground-based work to R $<$ 25.5 magnitudes. The
higher angular resolution provided by HST allows one to probe at least 2
magnitudes fainter, but the small field-size is a significant limitation. In
either case, our models show that the contribution from halo subdwarfs is
effectively limited to colours of (R-I) $<$ 1.0, with the redder stars being
members of the Galactic disk. The apparent increase in number density for M$_V
> 10$ in the derived luminosity function is a result of contributions from disk
stars at fainter absolute magnitudes and does not provide evidence for an
upturn in the halo subdwarf mass function. Indeed, starcount data alone are
{\it not} an effective method of probing the shape of the halo luminosity
function close to the hydrogen-burning limit. Finally, we examine how the
Hubble Deep Field observations can be used to constrain the contribution of
various stellar components to the dark-matter halo.
