This paper describes an acoustic class dependent technique for text independent speaker identification on very short utterances. The technique is based on maximum likelihood estimation of a Gaussian mixture model representation of speaker identity. Gaussian mixtures are noted for their robustness as a parametric model and their ability to form smooth estimates of rather arbitrary underlying densities. Speaker model parameters are estimated using a special case of the iterative Expectation-Maximization (EM) algorithm , and a number of techniques are investigated for improving model robustness. The system waa evaluated using a 12 reference speaker population from a conversational speech database, and achieved 89% average text independent speaker identification performance for a 1 second test utterance length.