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We propose an optimal method for designing multiplierless FIR filters with cascaded prefilter-equalizer structures. In particular, simultaneous design of multiplierless prefilters and equalizers based on cyclotomic polynomials (CPs) and interpolated second-order polynomials (ISOPs) with powers-of-two coefficients is introduced. After employing CPs for prefiltering and ISOPs for equalization, a cascade of the CP prefilter and the ISOP equalizer is simultaneously optimized by mixed integer linear programming (MILP). Design examples demonstrate that this method leads to more efficient cascaded FIR prefilter-equalizers than existing methods.