Systems based on i–vectors represent the current state–of–the–art in text-independent speaker recognition. Unlike joint factor analysis (JFA), which models both speaker and intersession subspaces separately, in the i–vector approach all the important variability is modeled in a single low-dimensional subspace. This paper is based on the observation that JFA estimates a more informative speaker subspace than the “total variability” i–vector subspace, because the latter is obtained by considering each training segment as belonging to a different speaker. We propose a speaker modeling approach that extracts a compact representation of a speech segment, similar to the speaker factors of JFA and to i–vectors, referred to as “e–vector.” Estimating the e–vector subspace follows a procedure similar to i–vector training, but produces a more accurate speaker subspace, as confirmed by the results of a set of tests performed on the NIST 2012 and 2010 Speaker Recognition Evaluations. Simply replacing the i–vectors with e–vectors we get approximately 10% average improvement of the C $_{\text{primary}}$ cost function, using different systems and classifiers. It is worth noting that these performance gains come without any additional memory or computational costs with respect to the standard i–vector systems.