  We propose a method to produce a definite number of ground-state atoms by
adiabatic reduction of the depth of a potential well that confines a degenerate
Bose gas with repulsive interactions. Using a variety of methods, we map out
the maximum number of particles that can be supported by the well as a function
of the well depth and interaction strength, covering the limiting case of a
Tonks gas as well as the mean-field regime. We also estimate the time scales
for adiabaticity and discuss the recent observation of atomic number squeezing
(Chuu et al., Phys. Rev. Lett. {\bf 95}, 260403 (2005)).
