A near-end crosstalk (NEXT) cancellation system that uses frequency-domain least-mean-squares (FDLMS) adaptive filters is proposed. The new system is equipped with a mechanism whereby the NEXT signals are detected and then FDLMS adaptive filters are assigned to cancel only the significant NEXT signals. The paper also explores various schemes of assigning step sizes to the adaptive filters. It has been found that by making the step sizes proportional to the magnitudes of the NEXT signals during the initial phases of adaptation, and equal later on, significant improvement in the convergence rate can be achieved. By returning after convergence to step sizes that are proportional to the magnitudes of the NEXT signals, a much better tracking performance can also be achieved.