1. An apparatus for reducing peak power in a transmitter for use in telecommunications system, by non-linear processing of an input main signal, where the apparatus comprises successive processing stages, each stage of said apparatus comprises: a peak finder to: find, in a present stage, at least one peak of said input main signal exceeding a predetermined threshold level, and make a list (L 0 ) comprising information on each found peak or information on a number of a largest found peak(s); a peak selector to: receive, from said peak finder, said list (L 0 ), receive, from each preceding stage, if any, a list (Li) comprising information on unreduced peaks and a stage number, select, from said lists (L 0 , Li), at least one peak (P) to be reduced, and determine based on said stage number, a fractional sample shift value (FSi) of the stage in which said selected peak (P) was initially found; a kernel selector to select, for each selected peak (P) to be reduced, a kernel signal (Ki) that is fractionally-sample shifted with a fractional sample shift value that is equal to a sum of all fractional sample shift values, starting from the determined fractional sample shift value (FSi) up to the present stage ( 10 ); a kernel manipulator to scale, rotate, and cyclically shift the fractionally-sample shifted kernel signal (Ki) based on information on the selected peak (P); and a combiner to reduce at least the selected peak (P) by generating a peak reduced signal through combination of the scaled, rotated, and shifted kernel signal (Ki) with a delayed version of the input main signal.