This brief introduces a design and implementation of maximally flat cascaded integrator comb compensation filters. In particular, we consider second- and fourth-order linear phase filters for narrow-band and wideband compensation. Closed-form equations for the computation of the filter coefficients are given. The multiplierless implementation is also considered. The number of adders is a function of the decimation factor D and the number of stages N. The implementation complexity is discussed, and comparisons with some methods reported in the literature are provided.