We discuss a quantizer which, for every new input sample, adapts its step size by a factor depending only on the knowledge of which quantizer slot was occupied by the previous signal sample [1]. Specifically, if the outputs of a uniform B-bit quantizer are of the form Yu = PuΔu2; ±Pu = 1, 3, ⋯, 2B − 1, Δu>0, the step size Δr is given by the previous step-size multiplied by a time-invariant function of the code-word magnitude |Pr−1|: Δr = Δr−1 ⋅ M(|Pr−1|). The adaptations are motivated by the assumption that the input signal variance is unknown. Computer simulations have shown that, for first-order Gauss-Markoff signals, the optimum multiplier function M (which minimizes the mean-squared value of quantization error) has the property that it calls for fast increases of step size but slow decreases thereof. This property was first observed in a differential speech quantizer described by Cummiskey and Flanagan during the previous meeting of the Acoustical Society. In fact, there is a remarkable agreement between the actual multiplier values used in the speech quantizer and the optimum multipliers noted in the present study. Furthermore, with a Gauss-Markov input, changes in input signal correlation have a very small effect on the values of optimum multipliers. This seems to indicate that the afore-cited speech quantizer is quite robust, although it was designed with a limited set of speech inputs.