In this study, we focus on nonlinear compression methods in spectral features for speaker verification based on deep neural network. We consider different kinds of channel-dependent (CD) nonlinear compression methods optimized in a data-driven manner. Our methods are based on power nonlinearities and dynamic range compression (DRC). We also propose multi-regime (MR) design on the nonlinearities, at improving robustness. Results on VoxCeleb1 and Vox-Movies data demonstrate improvements brought by proposed compression methods over both the commonly-used logarithm and their static counterparts, especially for ones based on power function. While CD generalization improves performance on VoxCeleb1, MR provides more robustness on VoxMovies, with a maximum relative equal error rate reduction of 21.6%.