  Nonequilibrium, ``fast switching'' estimates of equilibrium free energy
differences, Delta F, are often plagued by poor convergence due to dissipation.
We propose a method to improve these estimates by generating trajectories with
reduced dissipation. Introducing an artificial flow field that couples the
system coordinates to the external parameter driving the simulation, we derive
an identity for Delta F in terms of the resulting trajectories. When the flow
field effectively escorts the system along a near-equilibrium path, the free
energy estimate converges efficiently and accurately. We illustrate our method
on a model system, and discuss the general applicability of our approach.
