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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 Neel wall driven by the 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.