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In practical FIR digital filter applications it is often necessary to represent the filter coefficients with a finite number of bits. The finite wordlength coefficient restriction reduces the filter quality and increases the filter deviation. This increase can be reduced substantially if the optimal finite wordlength coefficients are used. Computing these coefficients is more difficult and can be slow. It was shown before that the computation time can be significantly reduced with the help of a lower bound on the deviation increase. Derivation of a new algorithm that uses a much better lower bound is the purpose of this paper. We consider the general case of a length N filter with a discrete set of allowable real coefficients and demonstrate the effectiveness of the new algorithm on a set of filter design cases. The results show that this algorithm reduces the computation times up to 3 times when compared with the previously best results. • Practical FIR filter implementations often require low bit filter coefficients. • Quantization of FIR filter coefficients reduces the filter quality. • Optimal finite wordlength FIR filter coefficients are much better. • Computing the optimal low bit coefficients can be computationally demanding. • A new faster algorithm for optimal finite wordlength FIR design is a solution. [ABSTRACT FROM AUTHOR]