This paper extends the evaluation of Hidden Markov Models with quantized parameters (qHMM) presented in [5] to the case of speaker adaptive training. In speaker-independent speech recognition tasks, qHMMs were found to provide a similar performance as the original continuous density HMMs (CDHMM) with substantially reduced memory requirements. In this paper, we propose a Bayesian type of adaptation framework for qHMMs to improve the speaker-specific acoustic modeling accuracy. Experimental results indicate that the proposed qHMM adaptation scheme provides a comparable performance as obtained with the Bayesian adaptation of CDHMMs in a noise-free test environment. In the presence of noise, on the other hand, the performance improvement due to qHMM adaptation is lower than obtained in the CDHMM case. In general, the adaptation gains are on a similar scale fact that confers to qHMMs a great practical value.