Controlling the position of a magnetic domain wall with electric current may allow for new types of non-volatile memory and logic devices. To be practical, however, the threshold current density necessary for domain wall motion must be reduced below present values. Intrinsic pinning due to magnetic anisotropy, as recently observed in perpendicularly magnetized Co/Ni nanowires, has been shown to give rise to an intrinsic current threshold J(th)(0). Here, we show that domain wall motion can be induced at current densities 40% below J(th)(0) when an external magnetic field of the order of the domain wall pinning field is applied. We observe that the velocity of the domain wall motion is the vector sum of current- and field-induced velocities, and that the domain wall can be driven against the direction of a magnetic field as large as 2,000 Oe, even at currents below J(th)(0). We show that this counterintuitive phenomenon is triggered by Walker breakdown, and that the additive velocities provide a unique way of simultaneously determining the spin polarization of current and the Gilbert damping constant.