  We report measurements of the spin susceptibility, $\chi\propto g_v g^*m^*$,
in an AlAs two-dimensional electron system where, via the application of
in-plane stress, we transfer electrons from one conduction-band valley to
another ($g_v$ is the valley degeneracy, and $m^*$ and $g^*$ are the electron
effective mass and g-factor). At a given density, when the two valleys are
equally populated ($g_v=2$), the measured $g^*m^*$ is smaller than when only
one valley is occupied ($g_v=1$). This observation counters the common
assumption that a two-valley two-dimensional system is effectively more dilute
than a single-valley system because of its smaller Fermi energy.
