Intersymbol interference degrades the performance of digital communication systems: A practical method of reducing this type of distortion is provided by transversal filter equalization at the receiver. Lucky has shown that, if the unequalized peak distortion is less than 100 percent, then theNfilter tap gains minimize the equalized peak distortion if the intersymbol interference contribution from the correspondingNdelays is set equal to zero. This correspondence presents two extensions of Lucky's theorem. The first states that if the peak distortion is greater than 100 percent, the conclusion of the theorem does not hold in general. A second theorem gives two conditions where the conclusion does hold.