  In the presence of spin-orbit scattering, the splitting of an energy level in
a generic small metal grain due to the Zeeman coupling to a magnetic field B
depends on the direction of B, as a result of mesoscopic fluctuations. The
anisotropy is described by the eigenvalues g_j^2 (j=1,2,3) of a tensor G,
corresponding to the (squares of) g-factors along three principal axes. We
consider the statistical distribution of G and find that the anisotropy is
enhanced by eigenvalue repulsion between the g_j.
