A multicarrier transmission system uses a set of carriers spaced apart in frequency with a number of bits being assigned to each carrier. A transmitter has a mapper which maps a data signal to a parallel set of constellation values. A frequency domain-to-time domain transform stage converts the set of modulated carriers to a time-domain signal. A peak detector detects when the time-domain signal exceeds a predetermined criterion. A constellation modifier modifies the constellation value of at least one of the carriers to reduce the crest factor of the transmitted signal. A carrier is selected for modifying on the basis of a number of bits allocated to that carrier. The constellation modifier can select an alternative constellation value by an iterative method or by calculation. The constellation modifier can operate entirely in the time-domain.