The current mediated domain-wall dynamics in a thin ferromagnetic wire is investigated. We derive the effective equations of motion of the domain wall. They are used to study the possibility to optimize the power supplied by electric current for the motion of domain walls in a nanowire. We show that a certain resonant time-dependent current moving a domain wall can significantly reduce the Joule heating in the wire, and thus it can lead to a novel proposal for the most energy efficient memory devices. We discuss how Gilbert damping, nonadiabatic spin transfer torque, and the presence of Dzyaloshinskii–Moriya interaction can effect this power optimization. V C 2011 American Institute of Physics. [doi:10.1063/1.3554202]