We define an adaptive delta modulator in which the adaptation of the step size mr at the rth sampling instant depends on the comparison of two channel symbols—the bits Cr and Cr−1 corresponding to the rth and (r−1)st sampling instants. Specifically, the ratio of mr to the previous step size mr−1 is +P or −Q depending on whether Cr and Cr−1 are equal or not. We indicate the step response of the delta modulator and present results on the simulation of the adaptation logic on a speech sample that was band limited to 3.3 kHz. On the basis of signal-to-error ratios, we note that the equations PQ = 1 and P = 1.5 define optimal adaptation characteristics for sampling frequencies of 20, 40, and 60 kHz, and also that PQ⩽1+ε(ε≪1) represents a strong condition for stability. Finally, we comment on the relative performance of the adaptive delta modulator and of logarithmic PCM, and find that at a 60-kHz sampling rate, the delta modulator achieves a 7 log-bit PCM quality.