  We perform a finite size scaling study of the three-dimensional Heisenberg
spin glass in the presence of weak random anisotropic interactions, up to sizes
L=32. Anisotropies have a major impact on the phase transition. The
chiral-glass susceptibility does not diverge, due to a large anomalous
dimension. It follows that the anisotropic spin-glass belongs to a Universality
Class different from the isotropic model, which questions the applicability of
the chirality scenario.
