The design of finite/wordlength finite impulse response, (FIR) digital filters is of much interest and importance in practical digital systems. In fixed-point implementations of digital filters, the designer is allowed only a finite number of bits for each coefficient. In general, the best choice for the finite wordlength coefficients is neither the truncated nor rounded infinite-precision values. A new method for quantizing cascaded subfilters to produce an overall filter that improves upon or compares favorably with the optimal quantized direct-form implementation is introduced. In particular, this method enhances performance in designs requiring deep stopband suppression, which is very common in applications. By cascading subfilters, it is possible to improve the stopband suppression. A difficulty with designing cascaded subfilters is the nonlinearity of the problem. A Taylor series approximation is used to develop a linear integer program for the optimal cascaded coefficients, improving the stopband suppression with no additional loss in the passband deviation.