The control of magnetic order in nanoscale devices underpins many proposals for integrating spintronics concepts into conventional electronics. A key challenge lies in finding an energy-efficient means of control, as power dissipation remains an important factor limiting future miniaturization of integrated circuits. One promising approach involves magnetoelectric coupling in magnetostrictive/piezoelectric systems, where induced strains can bear directly on the magnetic anisotropy. While such processes have been demonstrated in several multiferroic heterostructures, the incorporation of such complex materials into practical geometries has been lacking. Here we demonstrate the possibility of generating sizeable anisotropy changes, through induced strains driven by applied electric fields, in hybrid piezoelectric/spin-valve nanowires. By combining magneto-optical Kerr effect and magnetoresistance measurements, we show that domain wall propagation fields can be doubled under locally applied strains. These results highlight the prospect of constructing low-power domain wall gates for magnetic logic devices.