Folding band sharpening of the cascaded-integrator-comb filter results in a high passband droop. In applications requiring low passband deviation, the droop is reduced by connecting a low-order FIR compensator in cascade with the filter. In this Letter, the authors present a method for optimum design of compensators whose coefficients are expressed as sums of signed-power-of-two terms. The method is based on the minimisation of passband deviation, with specified total number of terms.