  In our numerical study, we identify the best conditions for efficient domain
wall motion by spin-orbit torques originating from the Spin Hall effect or
Rashba effect. We demonstrate that the effect depends critically on the domain
wall configuration, the current injection scheme and the symmetry of the
spin-orbit torque. The best identified configuration corresponds to a N\'eel
wall driven by spin Hall Effect in a narrow strip with perpendicular magnetic
anisotropy. In this case, the domain wall velocity can be a factor of 10 larger
than that for the conventional current-in-plane spin-transfer torque.
