  Driven barrier crossings are pervasive in optical-trapping experiments and
steered molecular-dynamics simulations. Despite the high fidelity of control,
the freedom in the choice of driving protocol is rarely exploited to improve
efficiency. We design protocols that reduce dissipation for rapidly driven
barrier crossing under two-dimensional control of a harmonic trapping
potential, controlling both trap center and stiffness. For fast driving, the
minimum-dissipation protocol jumps halfway between the control-parameter
endpoints. For slow driving, the minimum-dissipation protocol generically slows
down and tightens the trap as it crosses the barrier, resulting in both
significant energy savings and increased flux compared to naive and
one-dimensional protocols (that only change trap center). Combining fast and
slow results, we design protocols that improve performance at all speeds.
