Efficient implementation of adaptive echo and near end crosstalk (NEXT) cancellers in high-speed Ethernet transceivers continues to be a challenging problem. In our previous work, we proposed a new method based on word-length reduction technique to reduce hardware cost of the filter part in adaptive echo and NEXT cancellers. However, the high hardware cost of the weight update part in these adaptive cancellers was not reduced by the above method. This paper presents a new complexity reduction scheme for the weight update part in adaptive echo and NEXT cancellers. By reducing hardware cost of the weight update part, the overall hardware cost of these cancellers can be further reduced. It is shown that, by applying the proposed scheme to the 10 Gigabit Ethernet over copper (10GBASE-T) system, the hardware cost of adaptive echo and NEXT cancellers can be reduced by about 42.02% only with 1.5dB performance loss, compared with the traditional design.