This paper focuses on discriminative trainings (DT) applied to i-vectors after Gaussian probabilistic linear discriminant analysis (PLDA). If DT has been successfully used with non-normalized vectors, this technique struggles to improve speaker detection when i-vectors have been first normalized, whereas the latter option has proven to achieve best performance in speaker verification. We propose an additional normalization procedure which limits the amount of coefficient to discriminatively train, with a minimal loss of accuracy. Adaptations of logistic regression based-DT to this new configuration are proposed, then we introduce a discriminative classifier for speaker verification which is a novelty in the field.