In this paper we present a study on speaker verification showing achievable performance levels for both high quality speech and telephone speech and for two operational modes, i.e. text-dependent and text-independent speaker verification. A statistical modeling approach is taken, where for text independent verification the talker is viewed as a source of phones, modeled by a fully connected Markov chain, where the lexical and syntactic structures of the language are approximated by local phonotactic constraints. A first series of experiments were carried out on high quality speech from the BREF corpus to validate this approach and resulted in an a posteriori equal error rate of 0.3% in text-dependent as well as in text-independent mode. A second series of experiments were carried out on a telephone corpus recorded specifically for speaker verification algorithm development. On this data, the lowest equal error rate is 2.9% for the text-dependent mode when 2 trials are allowed per attempt and with a minimum of 2s of speech per trial.