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The existing q-Markov COVER realization theory does not take into account the problems of arithmetic errors due to both the quantization of states and coefficients of the reduced order model. All q-Markov COVERs allow some freedom in the choice of parameters. In this paper we exploit this freedom in the existing theory to optimize the models with respect to thes,_ finite wordlength effects. *Dept. of Systems Engineering, Research School of Physical Science,s, Australian National University Canberra, ACT 2601, Australia **School of Aeronautics and Aslmnautics, Purdue University, West Lafayette, IN 47907, U.S.A. PRECEDING PAGE BLANK NOT FILMED