This paper addresses the challenges of fitting Generalized Additive Models (GAMs) using penalized regression splines, particularly in terms of numerical stability and the handling of rank deficiency. The author proposes an improved method for multiple smoothing parameter estimation that incorporates a ridge penalty, allowing for the imposition of lower bounds on smoothing parameters and the use of mixtures of pre-specified and estimated smoothing parameters. The method is based on the pivoted QR decomposition and Singular Value Decomposition (SVD), which ensures good error propagation properties and robustness in the presence of numerical rank deficiency. The paper also discusses the computational efficiency of the method and compares it to existing methods, including treating GAMs as generalized linear mixed models. The effectiveness of the new method is demonstrated through simulations and practical examples, showing its ability to handle complex and challenging data sets more effectively than previous approaches.This paper addresses the challenges of fitting Generalized Additive Models (GAMs) using penalized regression splines, particularly in terms of numerical stability and the handling of rank deficiency. The author proposes an improved method for multiple smoothing parameter estimation that incorporates a ridge penalty, allowing for the imposition of lower bounds on smoothing parameters and the use of mixtures of pre-specified and estimated smoothing parameters. The method is based on the pivoted QR decomposition and Singular Value Decomposition (SVD), which ensures good error propagation properties and robustness in the presence of numerical rank deficiency. The paper also discusses the computational efficiency of the method and compares it to existing methods, including treating GAMs as generalized linear mixed models. The effectiveness of the new method is demonstrated through simulations and practical examples, showing its ability to handle complex and challenging data sets more effectively than previous approaches.