We consider a class of FIR filters defined by the first order difference routing digital filter (DRDF) structure and sums of two powers-of-two coefficients. A novel design method is developed for constructing high quality filters with reference to the min-max error criterion. This method is highly efficient in terms of computational time. Simulation studies show a large improvement over existing methods such as quantization. In some cases, the peak ripple magnitude over the stop and pass bands is reduced by up to 13 dB over the quantization method. These results are achieved even for cases involving small number of delays.