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Memoryless nonlinear transforms of random signals with Gaussian statistics are encountered in a variety of signal processing applications. A well-known criterion for the description of distortion errors is the Mean Squared Error (MSE) between the input and output signals of the nonlinearity. A different criterion which has been found to be useful especially in the field of multicarrier communications is the Signal-to-Distortion Noise Ratio (SDNR), which is based on the BUSSGANG decomposition of the output of the nonlinearity. It is shown that the SDNR optimum coincides with the minimum MSE solution, which simplifies the optimization of memoryless nonlinear functions with respect to SDNR. The results are applied to quantization and dynamic range reduction of Gaussian signals.