The most substantial effect of increasing the spacing up to 2.0 kcal mol -1 was that equilibration was accelerated (Figure ) for a given total simulation time. This was discussed by Rizzi. The effect is intuitive -reducing the number of windows increases the total sampling time per window for a given total simulation time. This produces faster relaxation for a given computational cost. This suggests that for slowly relaxing systems where replica exchange is not used, the thermodynamic speed should be made as large as possible without negatively impacting the MBAR estimate through insufficient overlap. A speed of 2.0 kcal mol -1 appears to work well for this system. This protocol is effectively a simplified version of those of Minh and Rizzi. We believe that it has a more rigorous basis than more empirical approaches which minimise free energy differences between windows, because it effectively targets equal divergences of the probability distributions between adjacent states. Adding a constant energy offset to a Hamiltonian would produce a free energy difference while maintaining perfect overlap, and therefore spacing states according to free energy differences has a weak theoretical foundation. This protocol requires that the λ schedule for the trial simulations is sufficiently dense to faithfully capture variations in σ ∂H ∂λ with λ. However, for a reasonably chosen alchemical path (e.g. a reasonable choice of soft-core) there should be no sudden changes in σ ∂H ∂λ with λ (Figure ) meaning that the initial λ schedule does not have to be particularly dense.