Linear single-input single-output discrete-time systems P(z) with unknown parameters, order and relative degree are considered, which are perturbed by biased sinusoidal disturbances. Under the assumption that the disturbance frequencies, the sign of the static gain P(1), the sign of either Re[P(e(i)(j omega))] or Im[P(e(i)(j omega))], for any disturbance frequency omega(i), are known, linear disturbance compensators are proposed which achieve exponential disturbance suppression. Such results are then locally extended to the case of disturbances with unknown frequencies. (C) 2017 Elsevier Ltd. All rights reserved.