  Using Monte Carlo techniques, Ising models with ferromagnetic
nearest-neighbor interactions on a simple cubic lattice are studied. At the
surface transition, the critical exponent $\beta_2$ of the edge magnetization
is found to be non-universal, depending on the edge and edge-surface couplings,
in contrast to the situation at the ordinary transition. Results are compared
to those for two-dimensional Ising magnets with chain and ladder defects.
