All devices realized so far that control the motion of magnetic flux quanta employ either samples with nanofabricated spatially-asymmetric potentials (which strongly limit controllability), or pristine superconductors rectifying with low-efficiency time-asymmetric oscillations of an external magnetic field. Using layered Bi2Sr2CaCu2O8+delta materials, here we fabricate and simulate two efficient nonlinear superconducting devices with no spatial asymmetry. These devices can rectify with high-efficiency a two-harmonic external current dragging vortices in target directions by changing either the relative phase or the frequency ratio of the two harmonics.