The current-induced motion of a magnetic domain wall in a quasi-one-dimensional ferromagnet with both easy-axis and easy-plane anisotropies is studied theoretically. We analyze the spin-transfer-induced torque on a sharp domain wall upon the flow of a dc electric current in the wire. The torque is shown to have two components; one of them acts as a driving force on the domain wall. The other torque component leads to changes to the domain-wall shape in that it forces the magnetic moments to diverge from the easy plane.