Interpolation methods frequently deal poorly with noise. Least-squares based interpolation methods can deal well with noise, as long as it is Gaussian and zero-mean. When this is not the case, other methods are needed. I use an iteratively-reweighted least-squares scheme to interpolate both regular and sparse data with non-stationary prediction-error filters. I show that multi-scale methods are less susceptible to erratic noise than single-scale PEF estimation methods. I also show how IRLS improves results for PEF estimation in both cases, and how IRLS can also improve the second stage of the interpolation, where the unknown data is constrained by the PEF.