For a few years now, the problem of session variability in text-independent automatic speaker verification is being tackled actively. A new paradigm based on a Latent Factor Analysis (LFA) model has been applied successfully for this task. However, using this approach, a large training corpus with several sessions per speaker is required. This constraint is hard to satisfy in many real applications. In this paper, we try to analyze if the LFA paradigm still holds even when the constraint of multiple sessions per speaker isn't satisfied. We propose to study two approaches. The first one consists in using the basic paradigm of the LFA model and the second one is founded on a new interpretation of the interaction between the session and the speaker. The experiments were carried out with NIST SRE 2005 and 2006 protocols. We show that even with only one session per speaker the gain obtained by LFA session compensation (with the two strategies) is still very important.