The voltages induced by nearby lightning strikes are a major cause of outages in power distribution systems. We compute such voltages taking into account the effects of the dart leaders that precede subsequent return strokes in both natural and rocket-triggered discharges. The results show that for stroke locations that are approximately alone, the line prolongation, the leader electric field change has a significant influence on the amplitude and shape of the induced voltages. The taking into account of the leader field in the coupling mechanism results in an improved agreement between theory and experimental induced voltage data from close triggered lightning obtained in 1986 on a test line at the NASA Kennedy Space Center