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The standard state-of-the-art backend for text-independent speaker recognizers that use i-vectors or x-vectors is Gaussian PLDA (G-PLDA), assisted by a Gaussianization step involving length normalization. G-PLDA can be trained with both gener- ative or discriminative methods. It has long been known that heavy-tailed PLDA (HT-PLDA), applied without length nor- malization, gives similar accuracy, but at considerable extra computational cost. We have recently introduced a fast scor- ing algorithm for a discriminatively trained HT-PLDA back- end. This paper extends that work by introducing a fast, vari- ational Bayes, generative training algorithm. We compare old and new backends, with and without length-normalization, with i-vectors and x-vectors, on SRE’10, SRE’16 and SITW.