A laser pulse with a specially tailored temporal power profile, instead of a conventional temporal shape or substantially square shape, severs an IC link. The specially tailored laser pulse preferably has either an overshoot at the beginning of the laser pulse or a spike peak within the duration of the laser pulse. The timing of the spike peak is preferably set ahead of the time when the link is mostly removed. A specially tailored laser pulse power profile allows the use of a wider laser pulse energy range and shorter laser wavelengths, such as the green and UV, to sever the links without appreciable damage to the substrate and passivation structure material located on either side of and underlying the links.