If we scale the experimental uncertainties σ i by a given value (q), in the pure wsLSSA, we will get the same scaling of the uncertainties ς i in the RDF since they are directly related by Eq. 16. However, in the regularized case, the relation is nonlinear due to the presence of the regularization parameter (Eq. 21). Thus, it is important to check the scalability of the corrected effective RDF uncertainties. To illustrate that, we scaled the uncertainties of the sM(s) for CCl 4 (Fig. ) by a factor of four and then calculated the RDF using rwsLSSA and regularization criterion from Eq. 26. The result is given in Fig. . As one can see, we indeed see an increase in the uncertainties with respect to the initial case. However, it is not a factor of four, but 1.6 (on average). Also, the uncertainties are rather uniformly distributed over the r-range. It is a result of the overregularization that is required by fine grids in r-space, which cannot be effectively counteracted by the correction in Eq. 21. Thus, we can recommend not choosing increments in r-space significantly below what is allowed by the Nyquist-Shannon-Kotelnikov theorem, as it will produce unreliable estimations for the RDF uncertainties. . Theoretical RDFs for tetrachloromethane (CCl 4 ), as obtained from the Eq. 28, and the rwsLSSA with the uncertainties as given in Fig. and scaled by a factor four (denoted as "noise×4"). The optimal values of the regularization parameter were obtained from the criterion from Eq. 26. The colored areas around the curves, with corresponding color coding, represent the uncertainties given by Eq. 16. All curves were divided by their maximal value, corresponding to the Cl. . .Cl peak height. The damping factor in each case was γ = 0.001 Å 2 .