Unlike Chap.  6 , this chapter focuses on non-parametric transformationsTransformation of both the response and the explanatory variables. TransformationTransformation of the explanatory variables uses the Generalized Additive ModelAdditive model (GAM), described in Sect. 7.2. The transformationTransformation of the response iteratively applies the variance-stabilizing transformationTransformation to residualsResiduals from the fitted GAM. The algorithm developed, which we call RAVAS, is a robust version of Tibshirani’s AVAS (Additivity and VAriance Stabilization). The developments are presented as a series of options written in pseudocode. In addition to robustnessRobustness, three options use initial manipulation of the data to improve convergence of the backfitting algorithm for the GAM. Section 7.4.8 introduces an improved procedure for the variance-stabilizing transformationTransformation (option trapezoid), a detailed description of which is in Sect. 7.4.9. Section 7.5 uses simulations to illustrate the important improvement provided by this option, whether robustnessRobustness is chosen or not. Section 7.6 introduces a graphical procedure, the augmented star plot, which indicates which combinations of options lead to satisfactory models. The chapter closes with further data analyses, comparisons of AVAS and RAVAS, and with references to some of the literature on non-parametric regression.