We report results from a speaker verification trial which used hidden Markov models (HMMs). In this trial, enrolled users of two self-service teller machines were asked to repeat random 4-digit phrases to gain access to their accounts. Use of a single speaker-specific HMM model resulted in a mean individual equal error rate (EER) of 18.4% for a population of 50 English speakers. This decreased to an EER of 10% when raw scores were normalized using a single cohort model built from an independent population. The performance is further improved to 4.5% by constraining the individual feature variances for all models to a fixed set of values. By doubling the training set size, the cohort normalized fixed variance system had a verification accuracy of 1.5% EER. For comparative purposes, we used the same technique on the publicly available YOHO speech corpus and obtained a mean EER of 0.4%.