Poor overlap, as indicated by large weight changes, can be improved by enhanced sampling methods that enrich the sample before refinement to better match the experimental observables, e.g., by using replica simulations. We then reweight the sampled ensemble using MBAR or binless WHAM to produce a reference ensemble for subsequent BioEn ensemble refinement, as we have proposed in Ref. 9. By doing so, we can remove any biases, e.g., due to a finite number of replicas. One can also directly bias the degrees of freedom determining the values of the observables, e.g., by using empirical force-field refinement, as described for example in Ref. 33. Also in this case, we can generate a reference ensemble by reweighting the sampled ensembles for subsequent BioEn ensemble refinement.