  Three planned astrometry survey satellites, FAME, DIVA, and GAIA, all aim at
observing magnitude-limited samples. We argue that substantial additional
scientific opportunities are within the reach of these mission if they devote a
modest fraction of their catalogs to selected targets that are fainter than
their magnitude limits. We show that the addition of ~10^6 faint (R>15) targets
to the 40 10^6 object FAME catalog can improve the precision of the reference
frame by a factor 2.5, to 7 micro-as/yr, increase Galactocentric distance at
which halo rotation can be precisely (2 km/s) measured by a factor 4, to 25
kpc, and increase the number of late M dwarfs, L dwarfs, and white dwarfs with
good parallaxes by an order of magnitude. In most cases, the candidate quasars,
horizontal branch stars, and dim dwarfs that should be observed to achieve
these aims are not yet known. We present various methods to identify candidates
from these classes, and assess the efficiencies of these methods. The analysis
presented here can be applied to DIVA with modest modifications. Application to
GAIA should be deferred until the characteristics of potential targets are
better constrained.
