A noise-reduction (NR) enhancement to the generalized multi-delay frequency domain algorithm (GMDF) involving minimal additional computations is presented. Findings are presented on the ability of the algorithm to suppress street, office, air-conditioning and car noise from the microphone signal in hands-free telephony. For an additional eleven N/P real multiplies and eight N/P real additions per output sample, where N is the block size and P is the amount of output samples per GMDF iteration, results show an average increase in echo return loss enhancement (ERLE) of 9 dB at low SNR (-5 dB) and 6 dB at higher SNR (15 dB).