Presented is an approach to modelling session variability for GMM-based text-independent speaker verification incorporating a constrained session variability component in both the training and testing procedures. The proposed technique reduces the data labelling requirements and removes discrete categorisation needed by techniques such as feature mapping and H-Norm, while providing superior performance. Experiments on Switchboard-II conversational telephony data show improvements of as much as 48% in detection cost with a single training utterance and 68% with multiple training utterances over a baseline system.