Discrete-time adaptive disturbance rejection is relevant to active noise and vibration control. In this paper we develop an adaptive feedback disturbance rejection algorithm, for minimum phase plants, that does not require a measurement of the disturbance and requires only minimal information about the plant, namely the first nonzero moving average coefficient from control to performance. We also prove Lyapunov stability and asymptotically perfect disturbance rejection for disturbances generated by LTI Plants.