In this work we revisit discriminative training of the i-vector extractor component in the standard speaker verification (SV) system. The motivation of our research lies in the robustness and stability of this large generative model, which we want to preserve, and focus its power towards any intended SV task. We show that after generative initialization of the i-vector extractor, we can further refine it with discriminative training and obtain i-vectors that lead to better performance on various benchmarks representing different acoustic domains.