  The Fermi surface of elemental bismuth consists of three small rotationally
equivalent electron pockets, offering a valley degree of freedom to charge
carriers. A relatively small magnetic field can confine electrons to their
lowest Landau level. This is the quantum limit attained in other dilute metals
upon application of sufficiently strong magnetic field. Here, we report on the
observation of another threshold magnetic field never encountered before in any
other solid. Above this field, $B_{\rm{empty}}$, one or two valleys become
totally empty. Drying up a Fermi sea by magnetic field in the Brillouin zone
leads to a manyfold enhancement in electric conductance. We trace the origin of
the large drop in magnetoresistance across $B_{\rm{empty}}$ to transfer of
carriers between valleys with highly anisotropic mobilities. The
non-interacting picture of electrons with field-dependent mobility explains
most results. Coulomb interaction may play a role in shaping the fine details.
