I-vector extraction and Probabilistic Linear Discriminant Analysis (PLDA) has become the state-of-the-art configuration for speaker verification. Recently, Gaussian-PLDA has been improved by a preliminary length normalization of i-vectors. This normalization, known to increase the Gaussianity of the i-vector distribution, also improves performance of systems based on standard Linear Discriminant Analysis (LDA) and "two-covariance model" scoring. But this technique follows a standardization of the i-vectors (centering and whitening i-vectors based on the first and second order moments of the development data). We propose in this paper two techniques of normalization based on total, between-and within-speaker variance spectra 1. These "spectral" techniques both normalize the i-vectors length for Gaussianity, but the first adapts the i-vectors representation to a speaker recognition system based on LDA and two-covariance scoring when the second adapts it to a Gaussian-PLDA model. Significant performance improvements are demonstrated on the male and female telephone portion of NIST SRE 2010.